Preheat oven to 350°F and line a baking sheet with parchment paper.
Melt the salted butter in a medium saucepan over medium heat, cooking past boiling until it turns golden brown and emits a nutty aroma. Stir constantly to prevent burning.
Pour browned butter into a bowl and chill in the refrigerator or freezer for about 10 minutes to cool.
In a mixing bowl, combine the cooled browned butter with brown sugar and granulated sugar until smooth.
Add the egg and vanilla and mix on low speed until fully incorporated.
Gently mix in the salt, baking soda, and flour, being careful not to overmix.
Fold in the rice krispie cereal followed by the mini marshmallows.
Scoop large balls of dough using a 3 tablespoon cookie scoop, placing 4 to 5 cookies per sheet to allow room for spreading.
Bake cookies for 10 to 13 minutes until edges are light golden brown, avoiding overbaking to preserve the chewy center.
Remove from oven and sprinkle with flaked salt before cooling slightly on the baking sheet.