Preheat oven to 350 degree F. In a medium mixing bowl stir together flour, cocoa powder, 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 1/2 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 8 minutes or until theyre just set and surface is slightly cracked. Let cookies stand for 1 minute. Transfer cookies to wire racks; cool. Place in layers separated by waxed paper in an airtight container; cover. Store at room temperature for up to 3 days or freeze for up to 3 months.
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