Preheat the oven to 350 degrees. Prepare two muffin pans with cupcake liners. Spritz the cupcake liners with nonstick cooking spray.
In a mixing bowl, whisk together the flour, sugar, brown sugar, baking powder, baking soda, and salt.
To the dry ingredients, add the melted butter and oil, beating until blended. The mixture will be thick like a cookie dough.
Mix the peanut butter into the dough until equally blended.
To the batter, add the eggs one at a time, beating well between each addition and scraping down the sides as needed.
Next, beat in the vanilla, sour cream, and buttermilk until evenly mixed.
Fold in the chocolate chips.
Using a large cookie scoop, fill the cupcake liners about ⅔ full.
Bake the cupcakes for 22 to 25 minutes or until a toothpick inserted in the middle returns clean.
Remove the cupcakes from the oven and allow to cool completely on a wire rack prior to frosting.
For the frosting: Beat together the peanut butter and butter until creamy. Add the powdered sugar and salt, beating until the mixture is smooth. Add the milk to the frosting, scraping down the sides, and beat until fluffy or about 1 minute.
Transfer the frosting to a piping bag and decorate the cookies as desired with frosting, melted chocolate, and/or chocolate chips.