Preheat oven to 350°F. Prepare 2 round 9-inch cake pans: grease pans, then line bottoms with a circle of parchment paper.
In a large bowl, cream together peanut butter, butter, and sugar until fluffy. Beat in eggs one at a time, then mix in vanilla.
1 cup creamy peanut butter, 8 tablespoons unsalted butter, 1 cup granulated sugar, 4 large eggs, 1 teaspoon pure vanilla extract
Mix in 1/3 of the flour. Scrape down the sides of the bowl and mix in 1/2 of the milk. Repeat with flour and milk, then end with remaining flour, mixing until batter is smooth.
3 cups self-rising flour, 1 1/2 cups whole milk
Pour into prepared pans and bake for about 30 minutes, until a toothpick inserted in the center comes out clean. Let cool on a rack for five minutes, then remove from pans and cool completely before frosting. (If you're in a hurry, tightly wrap the cakes in plastic wrap, then place in the freezer. The resulting steam will help keep them moist, and the chilling will make frosting the cake easier.)
For the frosting
Using a stand mixer or electric hand mixer, beat butter for 2 minutes, then slowly add powdered sugar, and cocoa powder while mixing on low. Add peanut butter, vanilla, and 4 tablespoons milk and beat on medium speed until combined and fluffy. If frosting is too thick, beat in more milk 1 tablespoon at a time.
16 tablespoons unsalted butter, 3 1/2 cups powdered sugar, 1/2 cup cocoa powder, 1/4 cup creamy peanut butter, 2 teaspoons pure vanilla extract, 4-8 tablespoons whole milk
To assemble
Place a small bit of frosting onto the center of your cake stand or plate. Set one layer of cake on top. (The frosting will keep the cake from moving around while you frost.) Dollop a scoop of frosting onto the cake and spread evenly over the top.
Add the second layer, making sure to center over the first layer. Dollop a big scoop of frosting on top. Spread evenly over the top, bringing any excess down the sides. Use more frosting as needed to fully cover the cake.
If desired, add piped decoration. Pile the chopped peanut butter cups into the middle or arrange around the edge. Let the cake rest so frosting can set before serving.
1 1/2 cups mini peanut butter cups
Notes
Make sure the cake layers are fully cooled before frosting, or the frosting will melt.
Store covered for 3-4 days at room temperature, or store in the refrigerator.