Preheat the oven to 375°F. Lightly grease (or line with parchment) two baking sheets.
To make the dough: In a medium-sized bowl, whisk together the flour, cocoa, baking soda and salt. In another medium-sized mixing bowl, beat together the sugars, butter, and peanut butter until light and fluffy. Add the vanilla and the egg, beating to combine, then stir in the dry ingredients, blending well.
To make the filling: In a small bowl, stir together the peanut butter and confectioners sugar until smooth. With floured hands or a teaspoon scoop, roll the filling into 26 one-inch balls.
To shape the cookies: Scoop 1 tablespoon of the dough (a lump about the size of a walnut), make an indentation in the center with your finger and place one of the peanut butter balls into the indentation.
Bring the cookie dough up and over the filling, pressing the edges together cover the center; roll the cookie in the palms of your hand to smooth it out. Repeat with the remaining dough and filling. Roll each rounded cookie in granulated sugar, and place on the prepared baking sheets, leaving about 2 inches between cookies. Grease the bottom of a drinking glass, and use it to flatten each cookie to about 1/2-inch thick
Bake the cookies for 7 to 9 minutes, or until they're set and you can smell chocolate. Remove them from the oven, and cool on a rack.