Preheat your oven to 350°F (175°C). In a large mixing bowl, cream together unsalted butter, creamy peanut butter, granulated sugar, brown sugar, and vanilla extract until smooth and fluffy, about 2-3 minutes.

In a separate bowl, whisk together the all-purpose flour, baking soda, and salt. Gradually add to the creamed mixture, stirring gently until just combined.

Scoop out spoonfuls of dough, roll into balls, flatten slightly, and place on a parchment-lined baking sheet, sprinkling tops with granulated sugar.

Bake for 10-12 minutes, until edges are golden and centers remain soft. Cool on sheet for 5 minutes before transferring to a wire rack.

In a clean bowl, beat together the filling ingredients until smooth. Adjust milk for texture.

Spread filling on the flat side of half the cookies and top with remaining cookies to form sandwiches.