In a large bowl, mix the flour and salt. Incorporate the cream cheese and butter using your hands until it forms a dough. Add the water and mix until all the flour disappears. Form the dough into a ball, flatten and wrap in plastic wrap, and refrigerate until ready to use.
Meanwhile, in a large bowl, combine the apples, sugar, vanilla, and lemon juice. Set aside.
On a floured surface, roll the dough into an even thickness about 1/8-inch thick by 12 inches diameter. Once the dough is rolled out, transfer to a 10-inch round tart pan. Using a fork, poke holes into the crust. Place the empty pie shell into the oven and par-cook for 10 minutes. Remove from the oven and let it cool. If the dough rises while cooking, just press it down with your hands.
Assemble the apples into the pie shell overlapping each other from the outside in. Pile the apples in layers. Pour the juice from the apples on the apples and cover with aluminum foil. Place the pan into the oven and bake for another 20 minutes.
Meanwhile, prepare the caramel sauce. Meanwhile, mix the sugar, heavy cream, butter and salt in a saucepan over medium-low heat. Cook while whisking gently for 5 to 7 minutes, until it gets thicker. Cook another minute to thicken further. Turn off the heat, cool slightly.
Turn the oven to broil. Remove the tart from the oven and pour the caramel sauce on top. Place the tart back into the oven directly over the broiler. Broil until the sugar turns golden brown, about 3 minutes. Remove the tart and cool for at least 15 minutes before cutting. Serve with vanilla ice cream.