Make the spice mix: combine chili powder, ground cumin, smoked paprika, garlic powder, onion powder, salt, and chipotle chile pepper in a small bowl; whisk to blend.
Pat the chicken thighs dry and rub lightly with a drizzle of olive oil, then season with about 1 1/2 tablespoons of the spice mix; reserve the remaining spice mix for the vegetables.
Heat 1 tablespoon olive oil in a large skillet or grill pan over medium-high heat and cook the chicken 3–4 minutes per side, or until an instant-read thermometer reads 165°F; transfer to a cutting board and let rest 5 minutes, then dice.
Wipe the skillet if needed, then heat the remaining 1 tablespoon olive oil over medium heat. Add the chopped onion and cook 3 minutes, stirring occasionally.
Add the chopped red bell pepper and the reserved spice mix; cook about 2 minutes until the pepper begins to soften.
Stir in the black beans, diced green chilies (if using), and minced garlic and cook 1–2 minutes more, until the onions are tender and peppers are crisp-tender.
Remove the skillet from the heat and stir in the diced chicken and half of the chopped cilantro.
Toss the Monterey Jack and cheddar cheeses together in a bowl for easy assembly.
Heat a 12-inch nonstick skillet over medium heat. Place one tortilla in the skillet and sprinkle 1/3–1/2 cup of the cheese mixture over half the tortilla, top with some of the chicken–vegetable filling and a sprinkle of cilantro, then fold the tortilla over to form a half-moon.
Press lightly with a spatula and cook until the bottom is golden and crispy, about 2–3 minutes.
Flip the quesadilla using the folded edge as a hinge, press lightly, and cook another 2–3 minutes until the second side is golden and the cheese is fully melted.
Transfer to a cutting board and cut into wedges with a pizza cutter; repeat with remaining tortillas, cheese, and filling. Serve immediately with salsa, guacamole, and sour cream or yogurt.
Optional keep-warm method: keep cooked quesadillas on a baking sheet in a 200°F oven until ready to serve.