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Preheat the oven to 375°F. Lightly grease (or line with parchment) two baking sheets.
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To make the dough: In a medium-sized bowl, whisk together the flour, cocoa, baking soda and salt.
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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.
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Stir in the dry ingredients, blending well.
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To make the filling: In a small bowl, stir together the peanut butter and confectioners' sugar until smooth.
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With floured hands or a teaspoon scoop, roll the filling into 26 small (1") balls.
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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.
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Bring the cookie dough up and over the filling, pressing the edges together to cover the center. Roll the cookie in the palms of your hands to smooth it out.
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Repeat with the remaining dough and filling.
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Roll each rounded cookie in granulated sugar, and place on the prepared baking sheets, leaving about 2" between cookies.
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Grease the bottom of a drinking glass, and use it to flatten each cookie to about 1/2" thick.
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To bake the cookies: 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.
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Storage information: Store leftover cookies, well wrapped, at room temperature for several days; freeze for longer storage.