For the pie dough:

1. Cut butter into small pieces and place back in the fridge.
2. Make ice water, strain, rescale.
3. Add to the mixer with the paddle attachment; flour, sugar, salt, butter and mix until the butter is pea sized.
4. Add ice water and vinegar, add to the mixer. Mix just until a solid piece of dough forms.
5. Place a dusting of all purpose flour on parchment paper and roll out 2 pieces of pie dough into a 14-inch round that is about the thickness of a quarter.
6. Sprinkle cheddar cheese on one piece of the dough, then lay the second piece of dough over the cheese and gently roll the two pieces together. Lightly dust the top layer of pie dough with flour to avoid sticking.
7. Cut into a 14-inch circle. Place dough with parchment on the sheet pan and put it in the fridge for at least 30 minutes

For the filling:

1. Slice the apples. I left the skin on but you can peel them.
2. Combine all the ingredients in a large mixing bowl and toss or stir until apples are completely covered with slices and flour.
3. Once dough is chilled, place apples in a pile in the middle of the dough leaving 2-3 inches of dough around the edges.
4. Fold the dough into the apples one piece at a time, overlapping each piece before the last.
5. Bush with egg wash and sprinkle with sugar.
6. Bake at 375 degrees until apples are soft and crust is golden brown, about 1 hour and 20 minutes. Check often. Bake until pie is golden brown.
7. Let cool slightly then serve with whipped cream or ice cream (al a mode).