Preheat the oven to 350F and line a baking sheet with parchment paper.
In a bowl, mix 1 cup of creamy peanut butter, granulated sugar, egg, and vanilla extract together until it forms a smooth, cohesive dough.
Roll the dough into small, 1-inch balls and place them on the baking sheet. Use a fork to gently press a classic crisscross pattern into each cookie.
Bake for 10-12 minutes until the edges are lightly golden. Let them cool completely on the baking sheet.
While the cookies cool, make the filling by beating the powdered sugar, softened unsalted butter, 2 tablespoons of creamy peanut butter, and milk until fluffy.
Once the cookies are cool, spread a generous spoonful of the peanut butter filling onto the flat side of half the cookies.
Top with the remaining cookies, flat side down, pressing gently to create sandwiches.