Directions

1. In a bowl, whisk together baking soda, salt, and 2 cups flour; set aside. In a large bowl, using an electric mixer, beat butter, brown sugar, and 1 cup peanut butter until light and fluffy; beat in egg. With mixer on low, gradually add flour mixture, beating just until combined (do not overmix).
2. Form dough into two 8-inch-long rectangular logs. Wrap each log in waxed or parchment paper; freeze until firm, about 1 hour.
3. Preheat oven to 350 degrees, with racks in upper and lower thirds. With a sharp knife, slice dough 1/4 inch thick; place on two baking sheets, 1 inch apart. Bake until cookies are puffed, 12 to 15 minutes, rotating sheets halfway through. Transfer to wire racks; let cool.
4. Make filling: In a saucepan, whisk milk and 2 tablespoons flour over medium until thickened, 2 minutes; let cool. In a bowl, using mixer, beat together 1/2 cup peanut butter and granulated sugar; beat in cooled milk mixture. Spread smooth sides of half the cookies with 1 tablespoon filling; sandwich with remaining cookies. (To store, keep in an airtight container, up to 5 days.)