Preheat oven to 375 degrees F. Line a baking sheet with parchment paper; set aside.
In a medium bowl, whisk together the flour, cocoa powder, baking soda and salt; set aside.
With an electric mixer on medium speed, cream together the butter, sugars and peanut butter until light and fluffy, about 3 minutes. Add the egg and vanilla extract and beat to combine. Reduce the speed to low, add the flour mixture and mix until combined.
In a separate medium bowl, mix together the peanut butter and powdered sugar for the filling until smooth.
In a small bowl, put some extra granulated sugar for rolling the cookies.
Use a medium cookie scoop (or heaping tablespoon) of cookie dough and flatten it with your hands. Take about 1 teaspoon of the peanut butter filling (or a small cookie scoop) and place it in the center of the chocolate dough. Wrap the chocolate dough around the peanut butter center, pressing to seal. Roll the cookie into a ball and roll in the sugar. Place the cookies on the prepared baking sheet about 2 inches apart. Flatten each cookie slightly with the palm of your hand.
Bake for 7 to 9 minutes. Let cool on the baking sheet for 2 minutes, then remove to a wire rack to cool completely. Store cookies in an airtight container at room temperature.