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1
Heat the oven to 350 degrees F and arrange a rack in the middle.
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2
Coat a 13-by-9-inch baking dish with butter; set aside.
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3
Fill a small saucepan with 1 inch of water and bring it to a simmer over medium-high heat.
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4
Place the chocolate in a stainless steel or glass bowl, set the bowl over the simmering water (be sure its not touching the water), and stir until the chocolate is completely melted, about 3 to 5 minutes; set aside to cool slightly.
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5
Combine the flour, cocoa powder, baking soda, and salt in a large bowl and whisk to aerate and break up any lumps; set aside.
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6
In the bowl of a stand mixer fitted with a paddle attachment, cream the measured butter and sugar on medium-high speed until light in color and fluffy, about 4 minutes.
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7
Add the eggs, 1 at a time, then the egg yolk, beating after each addition until evenly incorporated.
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8
Stop the mixer and scrape down the sides of the bowl using a rubber spatula.
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9
Add the vanilla and melted chocolate and return the mixer to medium-high speed, mixing until evenly combined, about 30 seconds.
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10
Reduce the speed to medium low and add a third of the reserved dry ingredients.
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11
When just incorporated, add half of the buttermilk.
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12
Repeat, scraping down the bowl at least once and ending with the last third of the dry ingredients.
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13
Pour the batter into the prepared dish, smooth the top with the spatula, and bake until a toothpick inserted in the middle comes out with only a few crumbs, about 35 minutes.
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14
Cool completely in the pan on a wire rack, about 1 hour.
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15
Meanwhile make the filling.
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16
Combine the cream, sugar, and egg yolks in a medium saucepan over medium heat, stirring constantly until the mixture thickens and coats the back of the spoon, about 8 minutes.
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17
Transfer to a medium bowl, add the remaining ingredients, and stir until the butter has melted and is evenly incorporated.
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18
Let cool to room temperature.
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19
Once the cake has cooled, carefully transfer it to a cutting board and slice it into thirds (the pieces should measure about 4 inches wide by 9 inches long), trimming as necessary to make the sections as even as possible.
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20
Spread about a third of the filling evenly over the top of 1 piece of cake, and another third of the filling over the top of a second piece.
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21
Stack the 2 pieces and place the last, unadorned piece on top.
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22
Set the last third of the filling aside.
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23
Using about a third of the vanilla buttercream, frost the sides and top of the cake.
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24
(Dont worry about looks at this pointthis is just a base coat, or crumb layer, and it will be covered up later.)
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25
Place the cake in the freezer for about 10 minutes, or the refrigerator for about 20 minutes, until the frosting is set up and slightly hard.
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26
Evenly spread the remaining frosting over the top and sides of the cake, then evenly spread the remaining third of the filling on top of the cake.
