Preheat oven to 350°F (175°C). Grease and flour two 9-inch round pans; line bottoms with parchment.
Whisk flour, baking powder, and salt in a bowl; set aside.
Beat butter and 1 cup sugar until light and fluffy, about 3–4 minutes.
Add 1/4 cup peanut butter and beat until incorporated.
Add eggs one at a time, beating after each; stir in vanilla.
Alternate adding dry ingredients and milk in three additions, beginning and ending with dry ingredients; fold in sour cream.
Divide batter between prepared pans and smooth tops.
Bake 25–30 minutes or until a toothpick in center comes out clean. Cool in pans 10 minutes, then remove to wire racks to cool completely.
Make frosting: beat butter and 3/4 cup peanut butter until smooth, add powdered sugar gradually and thin with milk to spreadable consistency; season with a pinch of salt.
Level cakes if needed, place first layer on board, spread a thin layer of frosting, stack second layer and crumb-coat. Chill 15 minutes, then finish frosting and smooth.
Chill briefly to set, slice, and serve. Store leftovers covered in refrigerator for up to 4 days.