Preheat your oven to 350°F (175°C).

In a large mixing bowl, combine softened butter, peanut butter, brown sugar, and granulated sugar. Blend on medium speed for 2-3 minutes until light and fluffy.

Beat in the egg and vanilla extract; mix on low speed for about 1 minute until well incorporated.

In a separate bowl, whisk together flour, baking soda, and salt.

Gradually add dry mixture to wet ingredients, mixing on low speed until just combined.

Scoop the dough into 1-inch balls and flatten slightly on a parchment-lined sheet.

Bake for approximately 10 minutes until edges are golden; allow cooling on the sheet before transferring to a wire rack.

Prepare the filling by beating together butter, peanut butter, powdered sugar, and vanilla. Adjust consistency with milk.

Once cookies have cooled, spread filling on one cookie and top with another to form a sandwich.