Season the chicken breasts with cumin, chili powder, garlic powder, and salt. Heat olive oil in a skillet over medium-high heat and cook the chicken for 6 to 7 minutes per side until cooked through. Let rest 5 minutes, then dice or shred the chicken.
Lay out the flour tortillas. Sprinkle a generous layer of shredded Mexican blend cheese on one half of each tortilla. Top the cheese with the diced chicken, diced red bell pepper, and sliced pickled jalapenos.
Add another layer of cheese on top of the fillings. This double cheese layer acts like glue to hold everything together. Fold each tortilla in half.
Melt about 1/2 tablespoon butter in a large skillet over medium heat. Place one or two quesadillas in the skillet and cook for 3 to 4 minutes on the first side until the tortilla is deeply golden and crispy.
Carefully flip and cook for another 3 minutes until the second side is golden and all the cheese is melted throughout.
Repeat with the remaining quesadillas, adding more butter to the skillet for each batch. Let them rest for 1 minute, then cut into wedges. Serve with sour cream and salsa for dipping.