Heat the oven to 375°F. Lightly grease a 9×13-inch baking dish and spoon 2–3 tablespoons enchilada sauce over the bottom to coat.
Warm the tortillas: stack and wrap them in foil and place in the oven for 5 minutes to soften; keep covered until assembly.
Flavor the sauce: In a small saucepan over low heat, stir together the enchilada sauce, ground cumin, and lime juice. Simmer gently for 3 minutes, then turn off the heat and keep warm.
Brown the beef: Set a large skillet over medium heat. Add the ground beef and onion and cook, breaking up the meat, until the beef is mostly browned and the onion is tender, 6–7 minutes. Spoon off excess fat, if needed.
Season the filling: Stir in the garlic and cook 30 seconds. Sprinkle the taco seasoning over the beef and cook 1 minute to toast the spices. Add the green chiles and water, reduce heat to medium-low, and simmer until thickened and saucy, 4–5 minutes. Stir in 1/4 cup of the warm enchilada sauce; taste and add salt if needed.
Assemble: Working with one warm tortilla at a time, lightly brush or dip one side in the warm sauce. Spoon 2–3 tablespoons of the beef mixture down the center and sprinkle about 2 tablespoons cheese. Roll snugly and place seam-side down in the prepared dish. Repeat with remaining tortillas and filling.
Top and bake: Pour the remaining sauce evenly over the enchiladas and scatter the rest of the cheese on top. Cover loosely with foil and bake for 12 minutes. Uncover and bake 3–5 minutes more, until bubbling; switch to broil for 1–2 minutes to blister the cheese lightly. Let rest 5 minutes before serving.
Serve hot with sour cream and cilantro, if desired.