Grease or line a 9x9 baking pan with parchment paper.
Make the brown butter: Cut the butter in small pieces and heat the butter in a large pot or dutch oven on medium heat for about 3-5 minutes until the butter turns an amber color. The butter will first foam and start to pop. Then, brown bits will begin to form in the bottom of the pan. Once browned and popping slows, it is ready. You should smell a nutty aroma.
While the butter is browning, separate the marshmallows. Remove 2 cups of the marshmallows and set aside.
Once browned, lower the heat to low and add the marshmallows you did not set aside (about 6 cups), vanilla extract, and salt to the pot. Use a nonstick spatula to stir the marshmallow mixture until completely smooth and melted.
Once melted, remove the pot from the heat and add the rice crispy cereal until completely combined.
Next, add the remaining 2 cups of the mini marshmallows to the pot and mix until combined. Stir the mixture until the marshmallows are just melting (we don't want them to fully melt, as we want gooey pools of marshmallow throughout the treats).
Transfer the cereal mixture to the prepared making dish and press it into an even layer in the pan. Pro Tip: Use parchment paper to press down the treats for easy clean up. Alternatively, you can put some nonstick spray on your hands to press the treats down.
Once cooled, cut and enjoy!