Beat together first 3 ingredients and 1/2 cup granulated sugar with an electric mixer on medium speed until creamy. Stir in egg and vanilla.
Combine flour, baking soda, and salt in a separate bowl. Slowly stir flour mixture into peanut butter mixture until fully incorporated.
Scoop dough onto prepared cookie sheets, 1 rounded tablespoonful at a time, about 2 inches apart. (Dough should yield about 24 cookies.) Press cookies flat with the back of a fork dipped into remaining 1 tablespoon sugar.
Sprinkle cookies with any remaining sugar, if desired, and bake 12 minutes or until golden brown around edges.
Remove from oven, and cool 5 minutes on pan; transfer to a wire rack to cool completely.
Spread about 1 tablespoon Creamy Peanut Butter Filling onto flat side of 12 cookies, and top each with another cookie, flat side down, to make a sandwich.