Place the cubed butter in the fridge while you assemble all your ingredients.
Preheat the oven to 350 degrees F.
In a food processor, place the flour, a pinch of salt, and 1 tablespoon sugar. Add the butter and pulse until the mixture looks like wet sand. Add the cold water and pulse again until the dough just begins to come together in a large lump. Pour the dough into the tarte pan and, using your fingers, press the dough into the pan, forming a crust. Refrigerate the crust while you prepare the apples.
Peel the apples, cut into quarters, core, and then slice thinly. Place in a bowl and toss with the lemon juice, the remaining 1 tablespoon sugar, cinnamon, and a pinch of salt. Remove the crust from the refrigerator and dump the apples onto the crust, spreading them evenly. Brush the whole tarte with melted butter and bake until the tarte is golden and the apples have cooked down a fair amount, about 1 hour. Cool for at least 15 minutes before cutting. Serve with vanilla ice cream.