In a food processor, pulse together the flour, cheese, hatch powder and salt. Add the butter and roasted hatch chile and process until it comes together into a dough ball. Form into a disk, wrap in plastic and refrigerate for 30 minutes.
Preheat the oven to 425ºF.
Remove the dough from the refrigerator and roll out into a 1/4-inch thick round. Press into a pie pan and trim the edge and reserve for the lattice. Place a piece of parchment paper over the dough and top with pie weights.
Place in the oven and bake for 16-18 minutes or until golden brown. Remove from the oven.
Whisk together the egg yolk and the water and brush all over the crust. Place back into the oven and bake for 2-3 minutes or until it is set.
In a saucepan, add the apples, hatch chile, lemon juice, melted butter, sugars, cinnamon, nutmeg and cornstarch. Bring to a hard simmer and cook, stirring constantly, for 3-5 minutes or until liquid has thickened. Let cool.
Reduce the oven heat to 375ºF.
With a slotted spoon, add the apple mixture into the pie crust.
Form the extra pie crust dough into a ball and roll out into a square. Cut into strips. Weave the dough strips onto the top of the pie to form a lattice cover. Brush the lattice with the egg mixture.
Place the pie into the oven and bake for 15-20 minutes or until the lattice is golden brown.