Preheat oven to 350°F (175°C). Grease three 8-inch round cake pans, line the bottoms with parchment paper, grease the parchment, then flour the pans. Tap out any excess flour. Set aside.
In the bowl of an electric mixer, sift together flour, sugar, cocoa powder, baking soda, baking powder, and salt. In a medium bowl, whisk together the eggs, buttermilk, coffee, oil, and vanilla. Add the wet ingredients to the dry ingredients and mix on medium speed for 2 minutes. Scrape the sides and bottom of the bowl, then mix for an additional 20 seconds. (The batter will be very thin.)
Divide the batter evenly among the prepared pans. Bake for 20 minutes, then rotate the pans in the oven. Continue to bake for about 12 more minutes, or until a toothpick inserted into the center comes out almost clean. Cool the cakes in the pans on wire racks for 20 minutes, then turn them out onto cooling racks to cool completely.
In a mixer with a paddle attachment, combine powdered sugar, peanut butter, butter, vanilla, and salt. Mix on medium-low speed until creamy, scraping down the bowl as needed. Add heavy cream and beat on high speed until light and smooth (do not overbeat).
Level the tops of the cake layers if necessary. Place one cake layer on a serving plate. Cover with 1 cup of peanut butter frosting and sprinkle 10 chopped peanut butter cups over the frosting. Top with a second cake layer, cover with another 1 cup of peanut butter frosting, and sprinkle another 10 chopped peanut butter cups. Place the final cake layer on top (face-down) and frost the cake with the remaining peanut butter frosting. Smooth the frosting as much as possible. Refrigerate the cake for at least 1 hour to set the frosting.
Place chopped chocolate in a 4-cup measuring cup. Warm the cream in a small saucepan over medium heat until it just comes to a boil. Pour the cream over the chocolate and let sit for 2 minutes. Whisk the mixture until completely smooth. Allow it to cool, whisking occasionally, until slightly thickened but still pourable.
Pour the ganache over the center of the cake, letting it flow over the sides. Top with the remaining 10 chopped peanut butter cups. Refrigerate for at least 30 minutes to set the ganache. Remove from the refrigerator about 20 minutes before serving.
Notes
Keep any leftovers in an airtight container in the fridge. It will stay fresh for up to 3 days. You can also freeze slices for up to a month.