Step 1

Cake: Preheat oven to 350°F. Brush a 9-by-13-inch or 8-by-12-inch baking pan with butter. Line with parchment, leaving a 2-inch overhang on long sides. Butter parchment.

Step 2

Whisk together flour, cocoa, baking powder, and salt. Combine eggs and granulated sugar in the bowl of a mixer fitted with the whisk attachment. Beat on high speed until thick and pale, about 4 minutes. Add flour mixture; beat just to combine. Add butter and vanilla; beat to combine. Add sour cream; beat until smooth.

Step 3

Scrape batter into prepared pan, smoothing top with a spatula. Bake until top springs back when lightly touched and a tester inserted in center comes out clean, 30 to 35 minutes (for 9-by-13-inch) or about 40 minutes (for 8-by-12).

Step 4

Let cool in pan on a wire rack 10 minutes. Using parchment overhangs, lift cake out of pan and let cool completely on rack. (Cake can be made to this point and stored at room temperature, wrapped in plastic, up to 1 day.)

Step 5

Frosting: Beat butter and peanut butter on medium-high speed until light and fluffy, about 2 minutes. Beat in confectioners' sugar until thick and fluffy. Remove from mixer; stir in sour cream by hand until frosting is silky and dense. Spread over cake; sprinkle top with peanuts. Frosted cake is best the day it's assembled, but can be refrigerated, wrapped in plastic, up to 1 day. Return to room temperature before serving.