In a bowl, beat the butter, peanut butter, and brown sugar until light and fluffy.
Add the milk and vanilla to the wet mixture and beat until well combined.
Add the flour, baking soda and salt to the wet and mix until just combined.
Place parchment paper in the air fryer basket (you may need to cut the paper to ensure the size fits perfectly).
Form dough into ~12-13 balls (1 tbsp [18 g] of dough each) and place on the parchment paper in the air fryer, leaving space in between each for spreading (you may need to do this in batches). Using a fork, press a crisscross pattern into each ball of dough. Air fry at 325°F (160°C) (or as close as your air fryer will get) for 5-6 minutes, until golden-brown (all air fryers can be different, so you may need to bake for less or more time depending on yours). Let cool before eating - they will firm up as they cool.