This recipe is super easy to make and was inspired by a dish I had when I lived in Phoenix, Arizona. While not as good as the real mexican cooks out west, it is very close. My family loves this dish and it is very economical to make.
Place chuck roast in large dutch oven. Pour red chile taco sauce or 2 cans medium enchillada sauce to pan; then add the 4 cans chopped green chiles. Place lid on dutch oven and bake at 325 degrees approximately 3 1/2-4hrs until fork tender. Time may vary according to the size of the roast, keep a check on the roast - do not let sauce and chiles burn.
Let roast cool slightly. Shred roast, removing fat, with two forks in same pan that it was cooked in. Mix shredded roast in with the sauce and green chiles that are in the pan.
Place the mixture length-wise at the narrow part of the flour tortilla, do not be skimpy but do not get too much in the tortilia. Fold sides inward and then fold up longways into a roll. After you have all the burritos completed, place in a 9x13 pan that has been lightly sprayed with a cooking spray. Pour the 2 cans of medium enchillada sauce over the top of the burritos and top with cheese. Cover and bake at 325 degrees approximately 30 minutes. Remove covering and bake until the cheese has slightly browned.
HINT: Spray the bottom side of the aluminum foil (side closest to the pan/cheese) and the cheese will not stick to the aluminum foil.