Preheat oven to 375 degrees. Line 3 standard 12-cup muffin tins with paper liners.
Make the cupcakes: Whisk flour, baking powder, salt, and baking soda in a medium bowl. Put butter and sugar into the bowl of an electric mixer fitted with the paddle attachment; mix on medium speed until pale and fluffy. Reduce speed to low. Mix in peanut butter. Mix in eggs, 1 at a time, and vanilla. Add flour mixture; mix until combined. Mix in sour cream.
Spoon scant 3 tablespoons batter into each muffin cup. Bake until pale golden and a cake tester inserted into centers comes out clean, about 13 minutes. Transfer to wire racks; let cool completely.
Make the frosting: Put cream cheese, confectioners' sugar, and butter into the clean bowl of a mixer fitted with the clean paddle attachment; mix on medium- high speed until pale and fluffy. Stir in peanut butter with a rubber spatula.
Spread 1 1/2 tablespoons frosting onto each cupcake. Refrigerate until frosting is firm, about 10 minutes. Using tines of a fork dipped in confectioners' sugar, score each top in a crosshatch pattern. Cupcakes can be refrigerated in single layers in airtight containers up to 2 days.