Place marshmallows on a cookie sheet with parchment paper and freeze for at least 2 hours before using. Keep marshmallows in freezer until ready to bake.
Preheat oven to 350 degrees F. Line 2 cookie sheets with parchment paper and set aside.
In a medium bowl, place the flour, baking soda and salt. Whisk and set aside.
In the bowl of a stand mixer, cream the butter and both sugars until light and creamy.
Add the peanut butter, egg, and vanilla. Mix well and scrape bowl. Add the dry ingredients and mix until almost incorporated.
Remove marshmallows from freezer and fold a heaping cup of marshmallows into the cookie dough.
Use a cookie scoop to shape the cookie dough into balls. Place a few inches apart on a prepared baking sheet. Place remaining cookie dough in the fridge to keep marshmallows cold until ready to bake.
Bake cookies at 350˚F for 11-12 minutes or until just set and edges are starting to brown. Allow cookies to cool completely on tray, about 10 minutes. Transfer cooled cookies directly to serving platter or airtight container.