Preheat the oven to 350 degrees F.
In a large saute pan, melt the butter. Add the apples and saute for 2 minutes. Add the sugars, lemon juice and flour. Continue to saute for 2 minutes. Season the apples with nutmeg, cinnamon, and salt. Mix thoroughly and remove from the heat. Mix in the pecans. Cool the mixture.
Cut the dough into 2 halves. Lightly dust a rolling surface with flour. Roll out each half of dough to 12 inches in diameter and about 1/8-inch thick. Fold one circle of dough in fourths. Carefully lift the dough and place in a 10-inch deep-dish pie pan. Unfold the pie dough and spoon the apples into the pie shell. Place the second round of dough over the apples. Using a sharp knife cut away the excess dough. Using your fingers, crimp the edges of the pie firmly to seal the dough completely. With the same sharp knife, make three slits, about 4 inches long and 2 inches apart, across the pie dough.
Place the pie in the oven and bake for 45 minutes. Remove the pie from the oven and sprinkle the cheese over the top. Return the pie to the oven and continue to cook for 8 minutes, or until the cheese is bubbly. Serve warm with vanilla ice cream.
In a mixing bowl, combine the flour, salt, and sugar. Add the shortening and work it in with your hands until the mixture resembles coarse crumbs. Add the water, 1 tablespoon at a time, and work it in with your hands. Add only as much as you need for a smooth ball of dough. Wrap the dough in plastic wrap and refrigerate for at least 30 minutes.