Salt and pepper the meat. Heat the oil in a large skillet and brown the meat at medium high heat for about 5 minutes.
Add the onions and minced garlic, spreading the pieces around the skillet and on top of the beef. Sprinkle the diced chiles on top of the onions, then the tomatoes on top of the peppers. Cover the skillet, turn down the heat to medium and cook for 10 minutes.
Uncover the skillet and mix all the ingredients, then cover and cook for another 5 to 10 minutes. Serves 3 to 4.
Tomatillo Salsa, for serving
Combine chiles, cheese, and cilantro in a medium bowl and toss to evenly mix.
Heat a seasoned cast iron skillet or a large frying pan over medium heat. Add 1 quesadilla and cook until soft, about 15 to 30 seconds.
Add 1/2 cup cheese mixture on one half, fold in half, and cook until cheese is melted and tortilla is golden brown, about 1 to 2 minutes. Repeat for remaining quesadillas. Cut each quesadilla into 4 wedges and serve with tomatillo salsa.