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For the cake: Heat the oven to 375 degrees F. Line two 9 1/2-by-14-inch jelly-roll pans with parchment paper, leaving 1 inch of paper hanging over on all sides (this will help you lift the cakes out of the pan after baking).
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In the bowl of a stand mixer fitted with the whisk attachment, whip the yolks and 1 cup of the sugar on medium speed until the mixture is thick and fluffy, 3 to 4 minutes.
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Add the vanilla and mix for 1 minute.
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Scrape into a medium mixing bowl and set aside.
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Wash the stand mixer bowl and whisk very well (even the smallest amount of yolk will prevent the whites from whipping properly).
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Put the whites and salt in the mixer bowl whisk at medium speed until he whites become frothy.
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Slowly add the remaining 1/2 cup plus 2 tablespoons sugar.
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Increase the speed to high and whip until the whites become glossy and almost firm (the whites should not become dry).
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Remove the bowl from the mixer.
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Sift the cocoa over the egg yolk mixture and gently fold in one-third of the whites (this will help to prevent overmixing).
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Add the remaining whites and carefully fold until there are no visible streaks of white.
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Divide the batter between the two pans.
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Smooth the batter evenly with an offset spatula.
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Bake the cakes just until they have risen and feel like soft marshmallows, 8 to 10 minutes.
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Transfer the pans to wire racks and let the cakes cool to room temperature.
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Chill the cakes until cold, about 30 minutes.
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While the cakes are cooling, prepare the buttercream.
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For the peanut buttercream: In the bowl of a stand mixer fitted with the paddle attachment, cream the butter and peanut butter on medium speed until fluffy, about 2 minutes.
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Turn the speed to low, add the confectioners' sugar, salt and vanilla and mix for another 2 minutes.
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Add the cream, turn the speed to high, and beat for 1 minute.
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Cover and set aside.
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When cooled, remove the cakes from the refrigerator.
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Gently lift one cake from the pan, using the overhanging parchment as handles, and place it on a cutting board.
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Carefully separate the paper from the cake.
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Lay a piece of parchment on top of the cake and quickly flip the cake over.
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Remove the parchment and replace with a clean sheet of parchment.
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With a rolling pin, firmly roll over the cake to even it out and thin it out.
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Trim each cake to a 12-by-9-inch rectangle.
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Place in the freezer for 15 to 20 minutes; this firms it up, and if the cake is stuck to the parchment this allows you to flip one more time to release the paper.
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Repeat with the remaining cake.
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Spread a thin layer of jelly over the surface of both cakes.
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Divide the buttercream between the cakes and spread it evenly over the jelly, leaving a border at the top of one long side.
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(The rolls look best when the cake layer and buttercream layer are the same thickness.)
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Begin rolling up the cakes, one at a time, starting at a long side.
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The first roll is the most important-keep it tight.
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Continue rolling toward the top.
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It's best to go slowly and carefully.
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When you completed rolling a cake into a log, place it in the center of a new sheet of parchment.
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Take the paper above the roll and cover the roll with a little overlap.
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Now take a flat-edge utensil, like a bench scraper or a long spatula, and force it underneath the roll and push tight.
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This helps fill in any air pockets in the roll.
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Chill the rolls 15 to 20 minutes or overnight before cutting them; the colder, the better.
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For the chocolate shell: Put the chopped chocolate in a heatproof bowl and set it over a pan with 3 inches of simmering water.
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When the chocolate is completely melted, stir in the butter and oil.
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Set aside in a warm place.
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Remove the paper from the rolls.
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With a sharp knife, cut each roll into 6 even pieces; each will be about 2 inches wide.
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Place a screen over a sheet pan to allow excess chocolate to drip off.
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Working with one piece at a time, place a piece into the chocolate shell.
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Flip the piece over using a fork.
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Lift it out of the chocolate and tap off excess chocolate before setting it on the screen.
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Continue until each roll is completely coated.
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Move each roll slightly on the screen during drying so it doesn't stick.
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Once dry, carefully lift off the rolls and arrange them on a sheet pan.
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The rolls can be eaten right away or refrigerated, covered, for up to 4 days.
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Let them come to room temperature before serving.
