In the bowl of a stand mixer fitted with the paddle attachment (or using a hand mixer), cream together the butter, peanut butter, granulated sugar, and brown sugar on medium speed until smooth and fluffy.
Add the egg and vanilla extract. Mix until fully incorporated.
In a separate medium bowl, whisk together flour, baking soda, and salt.
Add the dry ingredients to the peanut butter mixture. Mix on low speed just until the flour is fully incorporated; do not overmix.
Gently fold in the marshmallows, chocolate chips, and peanut butter chips until evenly distributed.
Cover the bowl with plastic wrap and refrigerate for 1 hour, or until the dough is firm.
When ready, preheat the oven to 350°F. Line a baking sheet with parchment paper.
Using a 2-tablespoon scoop, drop the cookie dough onto the lined baking sheet, leaving about 2 inches between each cookie.
Bake for 10 minutes, or until the edges turn a light golden color and the centers look set but still soft. Do not overbake.
Remove the cookies from the oven and let them cool on the baking sheet for 1 minute. Then transfer them to a wire rack to cool completely.