Melt the 4 tbsp unsalted butter in a large pot over medium heat, then cook for about 2 minutes, swirling often, until the milk solids turn amber. Stir in the 1 tsp fine sea salt.

Add 15 oz of the mini marshmallows to the pot and reduce heat to low. Stir constantly for 3 to 4 minutes until fully melted and smooth, then stir in the 1 tsp vanilla extract.

Remove the pot from the heat. Fold in the 6 cups puffed rice cereal and the reserved 1 cup mini marshmallows with big, slow strokes until the cereal is coated and the reserved marshmallows are just softened, about 30 seconds.

Press the mixture into a parchment-lined, greased 9x13 inch baking dish to about 1.5 inches thick using greased hands or a measuring cup. Let set at room temperature for 45 minutes to 1 hour.

Lift the slab out with the parchment, slice into 12 bars on a cutting board, and arrange cut-side up on a serving plate.