Lightly coat a 9x9-inch pan with non-stick cooking spray.
Line the pan with a foil or parchment paper sling, leaving an overhang for easy removal.
Lightly spray the lined pan again and set aside.
Place a large pot over medium heat.
Add the butter and allow it to melt completely.
Continue cooking the melted butter, stirring or swirling the pan occasionally, until the butter turns golden brown and develops a nutty aroma.
Remove the pot from the heat immediately once the butter is browned to prevent burning.
Add the sea salt and 8 cups of mini marshmallows to the browned butter.
Stir until the marshmallows are fully melted and the mixture is smooth.
If the marshmallows do not melt completely, return the pot to low heat briefly and continue stirring until smooth. Do not allow the browned butter to burn.
Add the vanilla extract and stir until fully incorporated.
Place the Rice Krispies cereal in a large mixing bowl.
Pour the melted marshmallow mixture over the cereal.
Stir gently until the cereal is evenly coated.
Add the remaining 2 cups of mini marshmallows while the mixture is still warm.
Fold gently until the marshmallows are evenly distributed.
Transfer approximately half of the cereal mixture to the prepared pan.
Lightly press the mixture into an even layer. Do not press too firmly, as this may make the treats dense.
Spread the dulce de leche evenly over the first cereal layer.
Add the remaining cereal mixture over the dulce de leche layer.
Lightly press the top layer into an even surface.
Allow the treats to set at room temperature until cooled and firm enough to slice.
Use the foil or parchment sling to lift the treats from the pan.
Cut into squares and serve.