In a medium bowl, combine the chili powder, cumin, garlic powder, onion powder, smoked paprika, salt, and black pepper. Pat the chicken breasts dry with a paper towel, add them to the bowl, and toss to coat every surface evenly in the spice mixture. Let rest for 5 minutes.
Heat a large skillet over medium-high heat, add the olive oil, and sear the chicken for 5-6 minutes per side without moving it, until golden and the internal temperature reaches 165°F (74°C). Transfer to a cutting board and rest for 5 minutes, then chop into small bite-sized pieces.
In the same skillet over medium heat, cook the sliced bell peppers and onion with a pinch of salt and pepper for 5-7 minutes, stirring occasionally, until softened and lightly caramelized. Remove from the pan and set aside, then wipe the skillet clean.
Combine the shredded Monterey Jack and sharp cheddar in a bowl and toss together until evenly mixed. Set aside near your assembly station.
Lay a flour tortilla flat, sprinkle about 1/3 cup of the cheese blend over one half leaving a 1/2-inch border, then layer on one quarter of the chicken, one quarter of the sautéed vegetables, and a small additional handful of cheese. Fold the tortilla over into a half-moon and press gently. Repeat with the remaining 3 tortillas.
Melt 1/2 teaspoon of butter in the clean skillet over medium heat, slide in one assembled quesadilla, and cook for 2-3 minutes per side, pressing gently with a spatula, until deep golden brown on both sides and the cheese is fully melted. Rest on a paper-towel-lined plate for 1 minute, then repeat with the remaining quesadillas.
Cut each quesadilla into 3 triangular wedges using a sharp knife or pizza cutter, arrange on a serving plate, and serve immediately with your choice of sour cream, guacamole, salsa, jalapeños, cilantro, and lime wedges.