Heat oven to 345°F (175°C). Grease and line two 9-inch round cake pans with parchment rounds; lightly dust the sides with cocoa or flour and tap out excess.
Start the ganache: Place chopped chocolate in a heatproof bowl. Warm cream in a small saucepan until steaming (just below a simmer), then pour over chocolate. Let stand 2 minutes, then stir until smooth and glossy. Set aside to cool to a thick, pourable consistency while you bake and frost.
Whisk the dry ingredients: In a medium bowl, combine flour, baking powder, baking soda, and salt.
Bloom the cocoa: In a separate bowl, whisk cocoa powder with the very hot coffee and instant coffee granules until completely smooth and lump-free; this intensifies the chocolate flavor. Cool 3–4 minutes until very warm but not scalding.
Make the batter: In a large bowl, whisk together granulated sugar, brown sugar, and oil until silky, 1 minute. Whisk in eggs one at a time, then vanilla. Whisk in sour cream until smooth and slightly thickened.
Combine: Add half the dry mixture to the wet and whisk just to incorporate. Stream in half the warm cocoa-coffee mixture. Repeat with remaining dry ingredients and cocoa mixture, whisking only until no flour streaks remain. Let the batter rest 5 minutes to allow bubbles to settle for flatter layers.
Bake: Divide batter evenly between the prepared pans and smooth the tops. Bake 28–33 minutes, rotating pans once halfway, until the centers spring back and a toothpick comes out with a few moist crumbs.
Cool completely: Set pans on a rack 15 minutes, then turn cakes out, peel away parchment, and cool fully before frosting.
Make the frosting: In a stand mixer with paddle (or a large bowl with a hand mixer), beat butter on medium-high until very pale and fluffy, 4–5 minutes, scraping bowl. Add peanut butter and beat 1 minute more. Mix in vanilla and salt. Add powdered sugar in 3 additions, alternating with milk, beating on low until combined after each, then on medium for 30–45 seconds to aerate. Adjust with a splash more milk for a smooth, spreadable texture.
Assemble: If needed, level the cake tops. Place one layer on a board and spread about 1/3 of the frosting over it, pushing to the edges. Top with the second layer, then apply a thin crumb coat over the top and sides. Chill 15 minutes to set.
Finish frosting: Apply a generous final coat and smooth the sides and top. Tip: For a glassy finish, warm your offset spatula under hot water, wipe dry, and glide it around the cake.
Drip and garnish: Stir the ganache; if too thick, warm 5–10 seconds; if too thin, let cool briefly. Spoon or pipe a drip around the top edge, then fill the center and smooth. Decorate with swirls of any remaining frosting, scatter chopped roasted peanuts, and add chopped peanut butter cups if using.