Preheat oven to 350 degrees. Line baking sheets with parchment paper or silicone mats.
In a medium bowl, whisk together the flour, baking soda, baking powder, and salt. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, beat the butter, cream cheese, and sugars until light and fluffy, about 2 minutes. Add the egg and egg yolk, then add the vanilla and beat to combine. With the speed on low, gradually add the flour mixture. Add the peanut butter cups and mix until just combined. Scoop by rounded tablespoons onto the prepared baking sheets.
Bake for 10-14 minutes (depending on your oven) until golden. Remove from oven and immediately (and gently) press a few mini marshmallows into each cookie. Cool for 2-3 minutes on baking sheets before transferring to a wire rack to cool completely.