Preheat oven to 350 degrees. Spread ½ cup of enchilada sauce in the bottom of a 9x13 baking dish. Set aside.
Add the beef to a medium skillet over medium heat and brown, crumbling the meat as it cooks.
When meat is crumbled, add the onion, garlic, and green chiles. Continue cooking until meat is fully browned. Drain grease.
Add the taco seasoning and 2 tablespoons of water to the meat mixture and stir well to combine.
Place the tortillas on a microwave safe plate and cover with a paper towel. Microwave for 20 seconds to soften the tortillas.
Place a spoonful of the beef mixture and a small handful of monterey jack cheese in the center of a tortilla. Roll up and place the enchilada in the prepared baking dish.
Repeat the process with the remaining tortillas, meat, and cheese.
Pour remaining enchilada sauce over the enchiladas and top with the shredded cheddar.
Cover dish with foil and bake for 25 minutes.
Let set for 5 minutes before serving.