In a large bowl combine butter, peanut butter, brown sugar, and granulated sugar and use an electric mixer (or stand mixer) to stir together on medium-speed until creamy and well-combined.
Transfer to 350F (175C) preheated oven and bake for 10-12 minutes. Allow cookies to cool for at least 10 minutes on baking sheet before transferring to cooling rack to cool.
Scoop a heaping 1 ½ Tablespoon-sized scoop of marshmallow fluff onto the center of the bottom of one cooled cookie. Top with another cookie and lightly press together to form a sandwich.