For the cake, grease three 8-inch cake pans and line the bottom of each one with a round of parchment paper. Grease the tops of the paper rounds, pressing down to help them adhere smoothly to the bottom of each pan.
Combine chocolate, cocoa powder, and boiling water in a 4-cup heat-proof glass measuring cup with a pour spout. Whisk until smooth. Set aside.
Sift together flours, baking soda, and salt into a medium-sized bowl. Set aside.
In the bowl of a standing electric mixer, beat the butter until creamy. Add brown and white sugars and beat on high speed until light and fluffy, about 3 minutes. Add eggs, one at a time, beating for at least 30 seconds after each addition and scraping down the sides several times to ensure even mixing. Reduce speed to medium and add sour cream and vanilla. Beat until combined. With the mixer on low speed, add about a third of the flour mixture, followed by about half of the chocolate mixture. Repeat, ending with the flour mixture. Beat until just combined, about 15 seconds. Remove bowl from the mixer and scrape the bottom and sides of the bowl with a silicone spatula, folding gently to combine.
Divide the batter evenly between the cake pans, smoothing as needed to spread batter to the edge of each pan. Place 2 pans on the lower-middle rack and 1 on the upper middle rack of an oven preheated to 350°F. Bake until a skewer inserted in the center comes out clean, about 20 to 23 minutes. Cool cakes on racks for 20 minutes. Run a thin spatula around the perimeter of each pan before inverting each cake onto a large plate. Peel off paper and reinvert each layer onto a cooling rack. Cool completely.
For the frosting, cream together peanut butter, butter, and vanilla. Blend in confectioners sugar and salt, mixing well to combine. Add the cream and beat on high speed until smooth, creamy, and spreadable.
Spread about 3/4 cup of the frosting between each cake layer. After placing the last layer atop the cake, spread a very thin layer of frosting on the top and sides the cake. Refrigerate the cake for 15 minutes before spreading the sides and top of the cake with remaining frosting.
Return the cake to the refrigerator for at least one hour before glazing.
About an hour before you plan to glaze the cake, prepare the ganache. Place chopped chocolate in a 2-cup heat-proof measuring glass with a pour spout. Set aside. Bring heavy cream to a boil in a small saucepan. Pour cream over chocolate and let sit for 2 minutes. Mix well until smooth. Add vanilla extract and stir to combine. Let sit for an hour before pouring.
Remove the frosted cake from the refrigerator. Stir ganache until smooth before pouring about half of the mixture onto the middle of the cake until it spreads just to the edges. Return the cake to the refrigerator for about 5 to 10 minutes before pouring on the remaining glaze and letting it flow down the sides. If needed, use a long metal spatula to spread the glaze to the edges. Puncture any air bubbles in the ganache with a needle.
Refrigerate the cake until the glaze fully sets, about an hour. Transfer carefully to a serving plate.