In a small bowl, combine the cornstarch and water and mix well. Set aside.
Melt the butter over medium-low heat in a small saucepan.
In a small bowl, mix together the cream, sugar and brown sugar until smooth. Pour into the melted butter, bring the mixture to a boil and stir in the cornstarch mixture. Keep stirring, about 2 to 3 minutes, or until the mixture thickens.
Remove from the heat and stir in the vanilla and sea salt. Set aside.
Peel and core the apples. Slice the apples and place them in a large bowl. Stir in the sugar, light brown sugar, flour, cinnamon and cornstarch. Toss with your hands to coat the apples well.
Sprinkle the lemon juice over the tops of the apples.
Roll out a bottom pie crust to about ⅛-inch thick and place into a 9-inch pie plate or 10-inch Dutch oven.
Spread the apples evenly over the crust. Drizzle about ½ cup of the caramel sauce over the apples.
Place the second crust on top. If using a solid crust, be sure it has at least 6 vent holes.
Whisk together the egg and water and brush over the top of the crust.
Place the pie in a preheated to 375 degrees F. Bake for about 50 minutes, or until the crust is set up and the pie is bubbling through. You may need to use a pie shield around the outside edges as it cooks to prevent it from burning.
Remove from the oven and let rest at least 2 hours. Cut and drizzle with the remaining caramel sauce. Serve.