Season the chicken: Toss the chicken pieces with the chili powder, cumin, smoked paprika, garlic powder, salt, and pepper until every piece is coated.

Sear the chicken: Heat 1 tablespoon of the olive oil in a large skillet over medium-high heat. Add the chicken in a single layer and cook for 6-7 minutes, stirring occasionally, until browned outside and cooked through to 165°F on an instant-read thermometer. Transfer to a plate.

Cook the peppers and onion: Add the remaining tablespoon of oil to the same skillet. Cook the onion and bell pepper over medium heat for 4-5 minutes until softened with a little color at the edges.

Finish the filling: Return the chicken to the skillet, add the lime juice and cilantro, and stir for 30 seconds. Scrape everything into a bowl and wipe the skillet clean with a paper towel.

Assemble the chicken quesadillas: Toss the Monterey Jack and cheddar together in a bowl. Lay a tortilla flat, scatter a small handful of the cheese blend over it, spread a quarter of the filling on top, add another handful of cheese, and cover with a second tortilla. Repeat to make 4 total.

Griddle until golden: Melt 1/2 tablespoon of the butter in the skillet over medium heat. Cook one quesadilla at a time for about 3 minutes on the first side, pressing gently with a spatula, until deep golden. Flip and cook 2-3 minutes more, until the second side is browned and the cheese is fully melted.

Rest, slice, and serve: Slide each quesadilla onto a cutting board and let it sit for 2 minutes before slicing. Cutting immediately lets the melted cheese run out. Slice into 6 wedges and serve with salsa and sour cream.