Start by cooking the veggies. In a large skillet, melt a good chunk of butter over medium heat and add the sliced onion. Cook slowly until softened, lightly golden, and caramelized. Add the sliced peppers and continue cooking until tender and cooked through. Remove from the pan and set aside.
Next, cook the chicken. Heat olive oil in the same skillet over medium heat and add the diced chicken breast. Cook until almost fully cooked through, then season with the sweet paprika, dried thyme, cumin, salt, and pepper. Let it cook for another 2 minutes so the spices coat the chicken well. If the pan starts sticking, add a small splash of water. Remove from heat and set aside.
For the guacamole, mash the avocados in a bowl and stir in the lime juice, cilantro, minced garlic, salt, pepper, and a drizzle of olive oil. Mix until creamy and well combined. Adjust seasoning to taste.
To assemble the quesadillas, heat a skillet over medium-low heat with a drizzle of olive oil. Place one tortilla into the pan and layer with the cooked peppers and onions, chicken, and a generous amount of both cheddar cheeses. Fold the tortilla over and cook low and slow until golden brown on the bottom, about 4 minutes.
Carefully flip and cook the other side until crispy and the cheese is fully melted. Remove from the pan and let cool slightly before slicing.
Serve warm topped with sour cream and homemade guacamole.