Preheat your oven to 350°F and line a cupcake tin with liners. Set aside.
In a large bowl, sift together the flour, baking soda, cocoa, and salt. Set aside.
In another bowl, combine both sugars and the butter. Use an electric mixer on medium-high speed to cream until light and fluffy. Add the eggs one at a time, beating for 30 seconds after each addition. Stir in the vanilla extract until well mixed.
Add half of the dry ingredients and ½ cup of milk to the sugar mixture. Mix on low speed until combined. Repeat with the remaining dry ingredients and ½ cup milk, mixing on low until well blended.
Fill the cupcake liners ⅔ full with the batter. Bake for 15-18 minutes, rotating halfway through, until a toothpick inserted into the center comes out clean.
Let the cupcakes cool in the pans on wire racks for 25 minutes, then remove them from the pans and place directly on the racks to cool completely (about one hour).
Frosting:
Beat together the peanut butter and butter until creamy.
Add the powdered sugar, beating until the mixture is smooth.
Add the milk to the frosting, scraping down the sides, and beat until fluffy or about 1 minute.