In a large bowl, beat the butter and both sugars with a hand mixer until fluffy. Beat in the peanut butter, egg and vanilla. Then, mix in the flour, baking soda and salt until just combined. Chill the dough for at least 30 minutes.
Preheat oven to 350 degrees. Line a baking sheet with parchment paper. Remove the dough from the refrigerator and roll into 1/2 inch balls with your hands and place dough balls on the baking sheet 1 inch apart. Using your thumb, press holes into each dough ball.
Fill a ziplock bag with the marshmallow fluff. Snip off the corner of the bag and pipe the fluff into each hole. Bake for 11-12 minutes. Allow to cool on the pan (they will cook on the pan for a few minutes after they're removed from the oven).
Microwave a few additional spoonfuls of peanut butter on high in 20 second increments until it reaches a liquid consistency. Drizzle over cooled cookies.