Trim large pieces of excess fat from roast and cut into 6 to 8 big hunks. Add onion, garlic and beef broth into the bottom of a 5.5 or 6-quart crock pot and nestle beef into mixture. Sprinkle in chili powder, cumin, garlic, salt and pepper and then place the lid on top and cook on low for 6 to 7 hours, or until beef shreds easily. Remove beef, shred and place into a large bowl with enough cooking liquid to make it juicy, but not so much that it’s dripping. Stir in green chiles. Discard remaining cooking liquid.
Preheat oven to 350°F then spray a 9x13 pan or two smaller pans with nonstick spray, spreading two tablespoons of enchilada sauce in the bottom. Divide shredded cheese in half, reserving half for topping the enchiladas.
Wrap half the tortillas in a damp paper towel and microwave for 30 seconds. Spread about ¼ cup of shredded beef across the center of each tortilla and top with 1 tablespoon shredded cheese and roll. Place seam side down in the prepared pan, then repeat with remaining ingredients. Pour remaining enchilada sauce on top, topping with remaining cheese.
Generously spray a large piece of foil with nonstick spray and place sprayed- side down on the pan. Bake for 20 minutes, then remove foil and bake for 5 to 10 more minutes or until cheese is melted and sauce is bubbly. Let rest for 5 minutes before serving with toppings.
To freeze: Wrap the unbaked enchiladas with plastic wrap and foil, then freeze. Thaw for 24 hours in the fridge then remove the plastic wrap, reapply foil that’s been sprayed with nonstick spray, and bake as directed above.