Preheat the oven to 350°F (conventional) or 325°F (convection). Spray two 9-inch cake pans and line with parchment circles.
In a medium bowl, sift together cake flour, baking powder, baking soda, and salt. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, beat butter, peanut butter, and sugar on medium speed until light and fluffy, about 3–4 minutes. Scrape down the bowl.
Add eggs one at a time, mixing well after each. Beat in vanilla extract.
With the mixer on low, add dry ingredients in three additions alternating with milk in two additions, beginning and ending with dry ingredients. Mix just until incorporated. Finish folding by hand if needed.
Divide batter evenly between prepared pans (about 585g per pan for 2 layers). Smooth tops.
Bake 20–22 minutes, or until a toothpick inserted in the center comes out with a few moist crumbs.
Cool in pans for 10 minutes. Run a knife around edges, invert onto wire racks, remove parchment, and cool completely before frosting.
Make the Buttercream
In a stand mixer fitted with the paddle attachment, beat butter on medium-high until smooth and lightened, about 2–3 minutes.
Reduce speed to low and add powdered peanut butter ½ cup at a time, mixing fully between additions.
Add powdered sugar ½ cup at a time on low speed until fully incorporated.
Add vanilla and smooth peanut butter. Mix on medium until cohesive and smooth.
Switch to whisk attachment. With a mixer on medium-low, slowly add cold heavy cream. Increase speed to medium-high and whip 1–2 minutes until light and fluffy.
Assemble
Place one cake layer on a cake stand. Spread about 1 cup buttercream evenly over the top.
Top with a second layer and refrigerate 15–20 minutes to set.
Frost top and sides with remaining buttercream. Smooth with a bench scraper or swirl decoratively. Garnish with chopped peanuts if desired.
Notes
Yield: 1 (9x13-inch) cake, 2 (9-inch) layers, or 24 cupcakes
Technique: Pull the cakes at 20–21 minutes for the softest crumb.
Storage: Keeps moist for 4 days refrigerated; serve at room temperature.