In a heavy cast iron pot, heat milk, cream, and 1 cup sugar in a saucepan. Cover top of cream mixture completely with prepared popcorn. When popcorn starts to melt into mixture, sprinkle some more popcorn on top. When the mixture starts to bubble, remove off of heat and set aside for 30 minutes so the popcorn infuses its flavor into the cream mixture.
Strain popcorn mixture through cheesecloth or a mesh strainer and squeeze the mushy popcorn flavor back into the cream mixture.
Whisk together the 1 cup sugar, vanilla bean, butter extract, and eggs in a bowl.
Still whisking, pour the cream mixture into the egg mixture and pour this back into the cleaned-out pan. Cook until cream thickens on medium-low heat (You don't want to over cook the eggs because it will leave an egg flavor. Do not leave unattended.)
With a silicone spatula, scrape vanilla beans off of the pot and keep stirring all the flavors together. If vanilla beans clump up just break apart on the interior of the pot. When mixture thickens, remove from heat.
Put pot into a bowl of ice water. Let cool completely.
Churn in an ice-cream maker according to manufacturer's instructions. Take bucket and put into freezer for at least 5 hours.
To prepare the Fleur De Sel Caramel sauce, mix butter, brown sugar, half-n-half, and salt in a saucepan over medium-low heat. Cook while stirring or whisking gently for 10 minutes allowing for the brown sugar to dissolve and for the mixture to thicken. Add vanilla and cook until it thickens further. Turn off heat and pour sauce into whatever you plan to serve it in. Allow cooling until the sauce is just warm. Serve over ice cream.