Preheat your oven to 350°F (175°C). Cream together unsalted butter and creamy peanut butter for 2-3 minutes. Gradually add granulated sugar, brown sugar, egg, and vanilla, mixing until combined.

In a separate bowl, whisk together all-purpose flour, baking soda, and salt. Slowly mix into the wet ingredients until the flour is just incorporated.

Using a tablespoon, scoop and shape the dough into balls. Place them on a baking sheet lined with parchment paper and flatten slightly. Optionally, sprinkle extra granulated sugar on top.

Bake for 8-10 minutes until edges are lightly golden and centers are puffy. Do not overbake.

Let cool on the pan for 5 minutes, then transfer to a wire rack to cool completely.

Beat together creamy peanut butter and unsalted butter for the filling. Gradually add powdered sugar and vanilla extract, mixing until fluffy. Add milk if necessary for spreadability.

Spread or pipe the filling onto one cookie and top with another, pressing gently to form a sandwich.