Preheat oven to 350℉ and line a large baking sheet with parchment paper.
In the bowl of a stand mixer, cream together the brown sugar, peanut butter, and room temperature butter until light and fluffy, about 2-3 minutes.
Add egg and vanilla, and beat until well combined, scraping down the sides of the bowl as needed.
Add flour and salt and beat again until just combined.
Divide the dough evenly into 12 balls and place evenly on the prepared baking sheet. Flatten each with your hands into roughly ½ inch thick disks.
Scoop 1 tbsp of marshmallow fluff into the center of each dough disk, then form a sealed ball of dough around the marshmallow fluff. Place seal side down on the parchment-lined baking sheet.
Bake in the preheated oven for 11-12 minutes. Remove from oven. The cookies will be uneven, so immediately reshape the cookies into circles with a round, greased cookie cutter or wide mouth jar. Allow the cookies to cool completely on the baking sheet before trying to lift them. Serve!