Dough. Cut the butter into the flour, salt and sugar until pea sized, stir in the ice water until it holds together, then wrap and chill at least 2 hours. Caramel. Melt the sugar in a heavy pan over medium heat, stirring, until deep amber. Whisk in the butter, then the cream, boil 1 minute and stir in the sea salt. Cool.
Crust. Roll the dough to a 12 inch circle, fit it into a 9 inch dish, crimp and freeze 15 minutes.
Filling. Heat the oven to 400 degrees F. Toss the apples with the lemon juice, sugars, spices, salt and flour, rest 10 minutes, then stir in 1/3 cup caramel.
Topping. Whisk the flour, oats, brown sugar, cinnamon and salt, then cut in the cold butter until crumbly.
Assemble. Brush the crust edge with egg and sprinkle with coarse sugar. Fill with apples, cover with topping and set a baking sheet on the rack below.
Bake. Bake 45 to 55 minutes until the filling bubbles and the topping is golden, covering with foil if it browns too fast. Cool 2 to 3 hours before slicing.