Whisk together the chili powder, cumin, smoked paprika, garlic powder, onion powder, salt, and chipotle chile pepper in a small bowl to make the spice mix.
Pat the chicken thighs dry, drizzle with a little of the olive oil, and rub to coat. Season the chicken with 1 1/2 tablespoons of the spice mix and reserve the remaining spice mix for the vegetables.
Heat 1 tablespoon olive oil in a large skillet or indoor grill pan over medium-high heat. Cook the chicken 3–4 minutes per side until an instant-read thermometer reads 165°F (74°C). 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 until beginning to soften.
Add the chopped red bell pepper and the reserved spice mix, and cook 2 minutes.
Stir in the black beans, diced green chilies (if using), and minced garlic; cook 1–2 minutes more until the onions are tender-crisp. Remove from heat and stir in the diced chicken and chopped cilantro.
Toss the Monterey Jack and sharp cheddar together in a large bowl for easy assembly.
Heat a 12-inch nonstick skillet over medium heat. Place one tortilla in the skillet and sprinkle about 1/3–1/2 cup of the cheese onto half of the tortilla. Top the cheese with some chicken and vegetable filling and a little cilantro, then fold the tortilla over to form a half-moon.
Lightly press with a spatula and cook 2–3 minutes until the bottom is golden and crispy. Flip using the folded edge as a hinge, press lightly, and cook another 2–3 minutes until the tortilla is golden and the cheese is melted.
Transfer the cooked quesadilla to a cutting board and cut into wedges with a pizza cutter. Serve immediately with salsa, guacamole, and sour cream or Greek yogurt.
Alternatively, keep finished quesadillas warm on a baking sheet in a 200°F oven while you finish cooking the rest.