Bouchon Bakerys Nutter Butters

Name: Bouchon Bakery's Nutter Butters
Ingredients: For the cookie dough; 2 cups all-purpose flour; 2 teaspoons baking powder; 4 teaspoons baking soda; 1 pound (4 sticks) butter, at room temperature; 2/3 cup creamy peanut butter, preferably skippy; 1 cup granulated sugar; 1 cup firmly packed light brown sugar; 2 large eggs; 1½ teaspoons vanilla extract; 1/3 cup coarsely chopped peanuts; 2½ cups quick-cooking oats; For the filling; ¼ pound (1 stick) butter, at room temperature; ½ cup creamy peanut butter, preferably skippy; 1 2/3 cups confectioners’ sugar