Preheat oven to 350°F. Line 2 cookie sheets with parchment or silpat baking mats.
Cream butter, peanut butter, and both sugars in the bowl of an electric mixer fitted with the paddle attachment. Add egg, vanilla, milk, and salt and baking soda. Mix until combined. Slowly add flour and mix until dough comes together.
Scoop 1 tablespoon sized balls of dough. Place on cookie sheet 2” apart. Press each cookie down with the tines of a fork to create the criss cross pattern.
Bake for 8-10 minutes, until they just begin to brown. Cool completely on cookie sheets.
Make the filling: beat butter and peanut butter until smooth using a hand mixer. Slowly mix in powdered sugar, mix until crumbly. Add both extracts. Start by adding 2 tablespoons of heavy whipping cream, then add more 1 tablespoon at a time until you have the desired thickness for filling.
Turn half the cookies upside dow and spread with filling. Sandwich with the remaining cookies.
Store in an airtight container for up to 3 days.