For Caramel
1 1/2 cups sugar
1 cup heavy cream
6 tablespoons unsalted butter, diced
1 teaspoon vanilla
1/2 teaspoon salt

For Apple Layer
5 cups apple slices (see note) from about 4 large Granny Smith apples
1 cup sugar
1 tablespoon freshly squeezed lemon juice
1 teaspoon cornstarch
1 teaspoon cinnamon
1/2 teaspoon nutmeg

For Crust and Crumble
3 cups all purpose flour
1 cup sugar
1/2 teaspoon salt
1 teaspoon baking powder
16 tablespoons (1 cup) cold unsalted butter, diced
1 egg
3 tablespoons heavy cream