the goods:
cookies:
1/2 cup (1 stick) unsalted butter, room temperature
1/2 cup creamy peanut butter
1/2 cup granulated sugar (plus 1/4 cup more for rolling)
1/2 cup packed light brown sugar
1 egg
1 teaspoon vanilla
1 and 1/4 cup all-purpose flour
1/2 teaspoon baking soda
1/2 teaspoon baking powder
filling:
1/2 cup (1 stick) unsalted butter, room temperature
2 cups confectioners' sugar
1-2 tablespoons milk
In a large bowl, using an electric mixer, beat butter, peanut butter, and sugars on medium-high until light and fluffy, about 1 minute. Lower mixer to medium and add egg and vanilla continuing to mix until combined. Turn mixer to low and add in flour, baking soda, and baking powder. Mix until combined. Refrigerate dough for 30 minutes.
Preheat oven to 375 degrees. Form chilled dough first into 1-inch balls, then into a log shape. Roll the log-shaped dough in granulated sugar and place on baking sheet 2 inches apart. Using a fork, press down on logs to form a criss-cross pattern. Pinch the center to create a peanut shape.
Bake for 6-7 minutes until edges are lightly golden. Cool on baking sheet 2 minutes, then transfer to a wire rack to cool.
Filling: In a large bowl beat butter and peanut butter together until smooth. Slowly add in powdered sugar and turn mixer speed up to medium and beat until smooth. Add milk, 1 tablespoon at a time until desired consistency is achieved.
Spread a heaping tablespoon of filling onto bottom side of half the peanut butter cookies and top with other half to create sandwiches.