Preheat the oven to 350º F.
In a bowl, add apples, hatch chiles, cinnamon, melted butter, and sugar. Mix well.
In another bowl, add the flour and salt and whisk to blend.
Use a pastry blender to cut in the cold butter until your mixture is crumbly.
Add the cheese, egg, and butter and mix gently to form a dough ball.
Split the pie crust dough ball in half and place each on a piece of wax paper. Place another piece of wax paper over the dough and use a rolling pin to roll to ¼ inch thickness.
Place the first crust into a greased pie pan. Press the crust gently into the pan.
Dump the apple and hatch chile mixture into the pie pan.
Roll the second crust out and place over the apple mixture.
Use your fingers to pinch the top and bottom crust together, slowly working around the pie crust edges.
Take a knife and make 2-3 slits on the top to vent steam.
Bake at 350º F for 40-45 minutes until the crust is golden and the apples are cooked.
Remove from the oven and allow cooling.