Heat the oven to 375°F and line two baking sheets with parchment. Beat butter, peanut butter, brown sugar and dough granulated sugar until smooth.
Beat in egg and vanilla. Whisk flour, baking soda and salt, then mix into the dough just until combined.
Divide the dough into 30 balls, roll in the remaining sugar and place 2 inches apart. Unwrap all chocolates before baking.
Bake one sheet at a time for 9 to 10 minutes, until lightly browned underneath. Immediately press one chocolate into the center of each cookie.
Cool on the sheets for 10 minutes, then move carefully to a rack and leave until the chocolates are firm again.