Freeze the marshmallows: Spread marshmallows on a parchment-lined baking sheet and freeze for 20 minutes.
Brown the butter: Melt butter in a saucepan over medium heat, stirring often. Cook until golden brown with a nutty aroma (8-10 mins). Immediately pour into a large bowl to cool for 20-30 minutes until fluid but not hot.
Mix wet ingredients: Add brown sugar, granulated sugar, and vanilla to the cooled brown butter. Mix with a spatula until combined and slightly fluffy. Do not overmix.
Incorporate egg: Add the egg and mix well until the mixture is smooth and syrupy.
Combine dry ingredients and fold: Whisk flour, baking soda, and salt in a medium bowl. Add this to the brown butter mixture and fold until mostly combined. Stir in crispy rice cereal and 3/4 cup (38g) of frozen marshmallows.
Portion and freeze dough: Use a 1.35-oz scoop to portion dough into balls. Place on a parchment-lined baking sheet and freeze for 30-60 minutes to harden the marshmallows.
Preheat oven and prep sheets: Preheat oven to 325°F (160°C) for thinner cookies or 350°F (175°C) for thicker cookies. Line two baking sheets with parchment paper.
Bake and cool: Place dough balls 3 inches apart on prepared sheets. Press 2 more frozen marshmallows on top, tucking them under the dough. Bake for 9-11 minutes (at 325°F) or 8-10 minutes (at 350°F) until lightly golden and soft.