In a large bowl, beat the butter and peanut butter with electric mixers until smooth.
Add both sugars and mix on low speed for about 3 minutes, until well combined.
Incorporate the egg and vanilla extract, continuing to mix on low speed for another minute.
In a separate bowl, mix the flour, baking soda, and salt.
Add the dry ingredients to the butter and egg mixture, mixing on low speed until just incorporated. Finish mixing with a rubber spatula.
Let the dough rest in the fridge for at least 30 minutes.
To fill the cookies, take about 3 tablespoons of dough and flatten it on your palm to form a disc about 8 cm in diameter and 0.5 cm thick.
Place a marshmallow in the center of the disc and wrap the dough around, sealing well. If cracks appear, press them with your fingers to close.
Repeat the process for all 12 cookies, then press some peanut butter chips on the surface of each dough ball.
Chill the cookies in the refrigerator while preheating the oven to 180°C.
Arrange the dough balls on baking sheets lined with parchment paper, spaced about 5 cm apart, with the sealed side down.
Bake for 10-11 minutes, turning the sheets halfway through. The cookies will crack slightly on the surface revealing the marshmallow.
Remove from oven and, if desired, sprinkle with some sea salt flakes.
Let the cookies cool on the sheet until they are firm enough to transfer to a wire rack.