Preheat oven to 350°F. In a medium mixing bowl stir together flour, cocoa powder, salt and baking soda; set aside.
In a large mixing bowl beat together butter, the 1/2 cup granulated sugar, brown sugar, and the 1/4 cup peanut butter with an electric mixer until combined. Add egg, milk, and vanilla; beat well. Beat in as much of the dry ingredients as you can with mixer. Stir in remaining dry ingredients by hand with a wooden spoon. Form chocolate dough into 32 balls about 1-1/4 inches in diameter. Set aside.
For peanut butter filling, in a medium mixing bowl combine powdered sugar and the remaining 3/4 cup peanut butter until smooth. Shape mixture into 32 (3/4-inch) balls.
On a work surface, slightly flatten a chocolate dough ball and top with a peanut butter ball. Shape the chocolate dough over the peanut butter filling, completely covering the filling. Roll dough into a ball. Repeat with the remaining chocolate dough and peanut butter filling balls.
Place balls 2 inches apart on an ungreased cookie sheet. Lightly flatten with the bottom of a glass dipped in the 2 tablespoons granulated sugar. Bake cookies in preheated oven for 12 minutes or until they’re just set and surface is slightly cracked. Let cookies stand for 1 minute. Transfer cookies to wire racks; cool completely. Save for later? No. Devour now? Yes.