Start by heating a tablespoon of oil in your skillet over medium-high heat. Sauté the sliced bell peppers and onions with a sprinkle of salt until softened. This takes about 5 minutes. Once done, transfer them to a plate to make room for the chicken.
Add another tablespoon of oil to the pan and stir in the chicken strips. Sprinkle on the seasoning mix of chili powder, cumin, and oregano. Stir occasionally and cook until the chicken turns golden and is fully done, which takes about 8 minutes. When ready, transfer it to the plate with the veggies.
Heat another tablespoon of oil in the skillet, warming one tortilla at a time. Add a generous layer of shredded Monterey Jack and cheddar to one half of the tortilla, then top it with the cooked chicken, vegetables, avocado slices, and scallions. Fold the tortilla in half.
Cook it on both sides until golden and crispy, about 3 minutes per side. Repeat the process for the remaining tortillas.
Slice each quesadilla into wedges and serve with sour cream.