For Crust: Combine flour, grated cheese, salt, and cayenne pepper in a large bowl; toss to blend ingredients. Using a pastry blender or two knives, cut butter bits and shortening into flour mixture until crumbly. Add the ice water and toss with a fork until the water is incorporated. Form dough into a ball and wrap in plastic wrap; chill for 1/2 hour. Roll out half the dough into a 10-inch round on a lightly floured surface; fit dough into a 9-inch pie tin, leaving a 1/2-inch overhang. Prick the bottom of the shell with a fork and chill while preparing filling.

For Filling: In a large bowl, combine the potatoes, diced cheese, flour, parsley, salt, and cayenne pepper. Toss until the potatoes and cheese are lightly coated with the flour; set aside. In a skillet, melt 2 Tablespoons of the butter. Saute the mushrooms for 5 minutes; remove from heat and set aside.

Heat oven to 425 degrees. Remove pie shell from refrigerator and spoon half of the potato mixture in the bottom of the shell. Top with mushroom mixture, then remaining potato mixture. Dot with remaining 2 Tablespoons butter. Roll out the remaining crust on a lightly floured surface. Place crust on top of pie. Fold top edges under bottom crust edges pinching together; flute edges. Using a sharp knife, cut several small air vents in center of crust.

Bake pie for 15 minutes. Reduce heat to 350 degrees and bake for 25 minutes or until pie is deep golden brown. Let pie cool for 5-10 minutes before cutting into slices.