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1
Place oven rack in middle position and heat oven to 350u00b0F. Line a 9- by 13-inch cake pan (or quarter sheet pan) with parchment, then lightly grease with vegetable oil or butter.
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2
In a small saucepan over medium heat, melt the butter. Take off the heat, and immediately whisk in peanut butter and vegetable oil until evenly integrated. Transfer the peanut butter mixture to a liquid measuring cup (for faster cooling and easier drizzling in Step 4).
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3
In the bowl of a stand mixer fitted with the whisk attachment, combine sugars, baking powder, baking soda, salt, and eggs. Mix on low speed until just moistened, then increase speed to high and beat until thick and fluffy and pale, about 8 minutes (could be longer if using a hand mixer).
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4
Reduce speed to low, and drizzle in peanut butter mixture; mix until evenly incorporated. Add flour; mix until just incorporated, then add buttermilk. Use a rubber spatula to fold the batter a few times (scraping the bottom and sides of the bowl), then transfer the batter into the prepared pan and evenly distribute it. The batter will be thick and creamy, almost fudgy.
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5
Bake until puffed and firm, about 28 to 32 minutes (or 210u00b0 F in the middle). A tester inserted into the middle of the cake should come out clean. Cool completely in pan before frosting.
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6
To make the frosting: In the bowl of a stand mixer fitted with the paddle attachment, beat cream cheese and butter on medium speed for 2 to 3 minutes, or until smooth and creamy, scraping the bowl once or twice. In a separate bowl, whisk together the cocoa powder and powdered sugar until evenly integrated and no lumps remain. With the mixer on low speed, slowly add the cocoa/powdered sugar and mix until well blended, then increase speed to high and beat until fluffy and creamy, about 15 seconds longer.
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7
To frost, spread the frosting evenly over the cake with a knife. Top with sprinkles, if using. Tightly covered, the cake will keep well for several days.
