Butter (or coat with non-stick spray) a 9x13 glass baking dish with 2-inch sides.
In a large pot, melt butter over medium-low heat. It will melt, then foam, then turn clear golden and finally start to turn brown and smell nutty. Stir frequently, scraping up any bits from the bottom as you do.
Once the butter is browned and bubbly, add the salt, vanilla, and mini marshmallows. Stir the ingredients using a silicone whisk or spatula until the marshmallows are completely melted.
Turn off the heat, remove the pot from the stove and immediately fold in the rice cereal. Make sure it's evenly coated.