Season and Cook the Chicken. Toss the 1 1/2 pounds bite-sized chicken pieces with 1 tablespoon of the olive oil, 1 teaspoon chili powder, 1/2 teaspoon garlic powder, 1/2 teaspoon onion powder, 1/2 teaspoon black pepper, 1 teaspoon salt, and 2 tablespoons lime juice. Heat the remaining 2 tablespoons of oil a large skillet over medium-high heat. Add the chicken in a single layer and cook 5–6 minutes, turning once, until golden brown and cooked through. Transfer to a bowl and set aside.
Sauté the Vegetables. In the same skillet over medium heat, add 1 tablespoon of oil. Add the 1/2 sliced onion and 1 sliced bell pepper and cook 4–5 minutes until softened and lightly caramelized. Remove from heat and add the cooked chicken, 2 sliced green onions, and 1/2 cup drained black beans (if using).
Assemble the Quesadillas. Heat a clean large skillet or frying pan over medium heat and lightly coat with cooking spray or a small amount of oil. Place one flour tortilla flat in the skillet. Spread a generous layer of cheese over half of the tortilla, then add a scoop of the chicken mixture on top of the cheese. Fold the empty side of the tortilla over the filling to close.
Cook Until Golden. Cook 3–4 minutes per side, pressing gently with a spatula, until the tortilla is golden brown and the cheese melts completely. Repeat with remaining tortillas, wiping the skillet between batches if needed.
Slice and Serve. Transfer the cooked quesadillas to a cutting board and use a pizza cutter or sharp knife to cut each into 3 wedges. Serve immediately with sour cream, salsa, and hot sauce.