Spray a 9×9-inch pan with non-stick spray and line it with a sling of foil or parchment paper to help with easy removal later. Spray the lining again to ensure nothing sticks. I always make sure to coat the corners well, since sticky cereal bars can be tough to lift out cleanly.
Place a large pot over medium heat and add the butter. Allow it to melt, swirling occasionally, until the butter foams and the milk solids turn golden brown, giving off a nutty aroma. Watch carefully to avoid burning. Remove the pot from the heat when the butter is perfectly browned.
To the browned butter (from Step 2), add the fine sea salt and 8 cups of the mini marshmallows. Stir thoroughly until the marshmallows are completely melted and the mixture is smooth. If needed, return the pot briefly to low heat to help with melting, but avoid overcooking or burning the marshmallows. Once smooth, stir in the vanilla extract for extra flavor.
Measure out the cinnamon sugar Rice Krispies cereal into a large bowl. Pour the melted marshmallow mixture (from Step 3) over the cereal and use a spatula or large spoon to mix until the cereal is evenly coated. While the mixture is still warm, add the remaining 2 cups of mini marshmallows and fold them in gently. I like adding the marshmallows at this stage so you get pockets of gooey goodness in every bite.
Take about half of the Rice Krispies mixture (from Step 4) and press it lightly but evenly into your prepared pan from Step 1. Once the layer is flat, spread the dulce de leche evenly over the surface to create a creamy caramel center.
Top the dulce de leche layer with the remaining Rice Krispies mixture (from Step 4), pressing gently to create an even layer. Allow the bars to set at room temperature until fully cooled, making them easy to slice and serve.