Chop the onion and the garlic.
Heat 1 tablespoon of the oil in a large skillet or non-stick pan. Cook the onion and the garlic for 2 minutes.
Cook beef: Add ground beef and brown well, breaking it up as it browns, 3-4 minutes until the onions are softened. Drain the excess grease if there is too much in the pan, but it shouldn’t be if the beef is lean.
Add the dried oregano, paprika powder, cayenne pepper, cumin, coriander, salt (½ to 1 teaspoon to taste), and pepper. Stir in the tomato paste and the water (Note 2). Add the drained black beans.
Cook beef filling: Stir well and cook on medium-low heat for about 5 minutes.
Chop the avocado in the meantime. Remove the pan from the heat and stir in the avocado and herbs.
Wipe the pan clean or use another one. Heat the pan and brush it with some of the remaining olive (Note 6).
Fill quesadillas: Place one tortilla in the pan, and add some cheese to one half of it. Top with some of the beef mixture and add more grated cheese. Fold the other tortilla half over the filling.
Fry the quesadilla lightly on both sides until golden. Use a spatula to turn the quesadillas to the other side carefully.
Repeat with the remaining tortillas and filling.
Serve immediately with tomatoes or tomato salsa, sour cream, and lime wedges.