Peanut Butter-Stuffed Cookies

1 c. creamy peanut butter

1/2 c. powdered sugar

1/2 c. creamy peanut butter

1/2 c. (1 stick) butter, softened

1/2 c. packed brown sugar

1/4 c. granulated sugar, plus more for rolling

1 large egg

1 tsp. pure vanilla extract

1 1/2 c. all-purpose flour

1/2 tsp. baking soda

1/2 tsp. kosher salt