Begin by buttering an 8x8 square pan and lining it with parchment or wax paper, leaving an overhang over two opposite sides.
In a large, deep pot over medium heat, melt the butter, swirling the pool often, until it browns, emits a nutty aroma, and begins to sputter (approximately 5 minutes).
Stir in the sweetened condensed milk, vanilla, and salt using a flexible spatula, ensuring you scrape up the browned bits from the bottom of the pot. Cook for two minutes, stirring constantly.
Turn off the heat, add 10 ounces of mini marshmallows, and stir until they are completely melted.
Remove the pot from heat and stir in the Rice Krispies until fully coated and combined. Then, gently fold in the remaining 1 cup of mini marshmallows.
Transfer the mixture to the prepared pan and use the back of a spatula (or buttered hands) to lightly and evenly flatten the treats.
Allow the treats to set up on the counter for at least an hour before cutting them into 9 pieces of pure delight.
Store the Brown Butter Rice Krispie Treats in an airtight container at room temperature for up to 3 days. You can also freeze them for up to 3 months.