Melt butter in a saucepan over medium-high heat. Stir brown sugar, cream, and corn syrup into butter; cook, stirring, until mixture becomes thick and syrupy, 7 minutes. Stir 2 teaspoons salt into butter mixture. Remove from heat and add marshmallows; stir until marshmallows are smooth and melted.
Pour marshmallow mixture over rice cereal and stir. Transfer cereal mixture to prepared baking dish and press down with greased parchment paper. Sprinkle with 1/2 teaspoon sea salt; cool and cut into squares.
