Preheat oven to 350 degrees F. In a food processor, combine the graham cracker pieces, brown sugar and butter. Pulse until moistened fine crumbs form. Press the crumbs evenly onto the bottom and sides of a 9-inch pie plate. Bake in the preheated oven for 10 minutes, or until lightly browned. Let cool. Increase oven temperature to 425 degrees F.
Pour the sweetened condensed milk into the bottom of a glass baking dish and sprinkle sea salt over top. Cover dish tightly with foil. Place the baking dish inside a roasting pan and fill the roasting pan with 1 inch of hot water. Bake in the preheated oven for 2.5 hours, stirring every 30 minutes and replenishing water in roasting pan as needed. Let cool, stirring occasionally.
Pour the caramel filling into the prepared crust. Spray plastic wrap with cooking spray and place it over the pie, sprayed-side down. Chill in the refrigerator until the filling is set, about 4 hours.
In a medium bowl, combine the heavy whipping cream and confectioners’ sugar. Using an electric mixer, beat on medium speed for 5-6 minutes, or until it becomes firm. Remove plastic from pie and mound the whipped cream onto the pie. Cut into wedges and serve.