For the Birria Beef

1. Set your oven to 350 degrees F. Place Hatch red chiles onto a baking sheet spread out into a single layer. Toast in the oven for about 5 minutes, or until puffy. Remove and cool for 5 minutes. Tear off and discard the stems, shaking out the seeds and discarding them as well. Place the chile pods into a bowl and add just enough water to cover and soak the chiles. If necessary, place an additional bowl over the top to keep the chile pods submerged. Set aside. Leave the oven on.
2. Set a heavy bottomed pot or Dutch oven over medium heat. Add the vegetable oil. Blot all beef cuts with paper towels, then season all sides generously with salt, pepper and green chile powder. Working in batches, sear the beef on all sides, then remove to a plate. Turn off the heat to the Dutch oven.
3. Place the soaked chile pods, 1 cup of water from the chiles, cloves of garlic, whole cloves, cinnamon, oregano, cumin, and tomato sauce into a blender. Blend until pureed, adding more chile soaking water as necessary, to make a sauce.
4. Pour roughly 1/2 cup chile sauce into the bottom of the Dutch oven (or enough to coat the bottom). Place all cuts of beef into the pot, and pour out the remaining chile sauce all over the beef. Place onion quarters and bay leaves around meat cuts. Add just enough water to cover the beef. Cover with a well fitting lid and place beef into the preheated oven and cook for about 4 and 1/2 hours or until beef is very tender and falling off the bone.
5. Scoop out the Birria beef, leaving the sauce in the pot, and place into a large bowl. Discard the onion, bay leaves and any large fat pieces from the beef, and shred the meat. Cover Birria beef and set aside. What sauce is left in the pot will become the dipping sauce for the tacos. Season with salt and pepper to taste. Stir in any additional water (or beef broth) to thin to a desired consistency. Keep warm by setting Dutch oven over low heat with the cover on.

To Make Birria Quesatacos

1. Set a cast iron skillet or other non-stick skillet over medium high heat. Dip both sides of a corn tortilla into the top of the Birria sauce, (where all the really red fat is sitting) and place into the skillet. Sprinkle one-half of the tortilla with cheese, chopped onion, and Birria meat. Fry for about 2 minutes, or until the tortilla begins to darken. Fold the tortilla in half over the meat and fry both sides for an additional 30 seconds to crisp. Remove and repeat to make more tacos. Sprinkle with fresh cilantro and serve with a side of Birria sauce and lime wedges.