Spray an 9-inch square cake pan with nonstick spray.
Add the cereal to a large heatproof bowl and set aside.
Add the butter to a medium saucepan over medium-high heat. Cook until butter turns a light brown color and develops a nutty, toasty scent. Stir in the brown sugar, heavy whipping cream and corn syrup. Cook until thick and syrupy while stirring frequently, about 5-7 minutes. Stir in the salt. Turn the heat to the lowest setting and stir in the 10-oz bag of marshmallows, immediately removing the marshmallow mixture from the heat when it is smooth and melted.
If you'd like a totally smooth marshmallow mixture, add the remaining cup of marshmallows now and stir until melted. But if you'd prefer chunks of marshmallow in your Rice Krispies treats, wait a minute or two for the mixture to cool down before stirring in the remaining cup of marshmallows.
Quickly pour the caramel marshmallow sauce over the cereal and stir all together. Pour into the prepared pan and press down with a piece of parchment paper sprayed with nonstick spray. Take care to press lightly; if you press too hard, you will get dense, hard Rice Krispies treats. Sprinkle lightly with flaky sea salt.
Cool completely, and then cut into squares, oiling your knife if necessary to prevent sticking.
Store in an airtight container.