Start by bringing about 6 cups of water to a boil and setting a comal, griddle or cast-iron skillet on high heat. Set a frying pan on another burner, add the oil and turn the heat to medium.
When the comal is hot, set the quartered onions in the center, the unpeeled garlic on the edges and the chiles and tomatoes wherever there is room. You goal is to char the cut sides of the tomatoes and onions, and the skins of the chiles and garlic.
When the water boils, add salt and the nopales. Boil these for 10 minutes, then add a pinch of baking soda. The water may well froth a lot, so keep an eye on things so it doesn't boil over. Boil the nopales for a total of 15 to 20 minutes. Drain and rinse in cold water.
As everything else is either charring or boiling, brown the ground meat in the frying pan. It should be nicely browned by the time the nopales and vegetables are ready. If it's done early, drop the heat to low.
Once the nopales are cooked and rinsed, add them to the pan with the meat. Once the vegetables are nicely charred, remove the skins from the chiles and garlic, roughly chop the onions and put it all in a molcajete or food processor with the oregano and process into a chunky salsa. Add this to the pan with the meat and nopales.
Stir well and cook it all over medium-low heat while you heat up the tortillas on a comal or in a microwave, over the burners or whatever. Once everything's all ready, serve the carne con nopales with a slotted spoon to drain off any excess moisture and top with the cheese and cilantro. Serve with the lime wedges.
Notes
Prep time assumes you have pre-cleaned nopales.
Tips and Variations
To make this vegetarian, skip the meat, or better yet, replace the meat with chopped mushrooms.
If you prefer, these are also good on flour tortillas.
You could skip the fire-roasted salsa and go with a red chile sauce, like the one in my recipe for carne con chile, or for my red enchiladas.
You could go green here and replace the tomatoes with tomatillos, and add a roasted poblano or Anaheim chile to the salsa.