Heat 1 tablespoon olive oil in a large skillet over medium-high heat for about 1 minute. Add your diced chicken breasts and cook for 5-6 minutes, stirring occasionally. The chicken should be completely cooked through with no pink inside. This is where most people rush, but patience here makes everything better.
Sprinkle the cumin, garlic powder, salt, and black pepper over the chicken while it's still in the pan. Stir it all together and let it cook for another 30 seconds so the spices really coat the meat. You'll smell that amazing cumin aroma—that's when you know it's perfect.
Add the diced red bell pepper and fresh cilantro to the chicken mixture. Squeeze the lime juice over everything and stir until combined. Let this sit in the pan for about 1 minute while you grab your tortillas and cheese.
Remove the chicken mixture from the skillet and set it aside on a plate for a second. You don't need to wash the pan—we're using it again. Pat the skillet dry with a paper towel since we want it clean but still hot.
Place one flour tortilla on a cutting board or plate. Spread about 1/4 cup of the cheese on one half of the tortilla in an even layer. Add 2-3 tablespoons of the chicken mixture on top of the cheese, then fold the tortilla in half. Your quesadilla is basically ready to cook now.
Melt about 1/2 tablespoon butter in the skillet over medium heat. Once it's foamy, carefully place your first quesadilla in the pan and cook for 2-3 minutes until the bottom is golden brown and crispy. You'll hear it sizzle, which means it's working perfectly.
Flip the quesadilla carefully using a wide spatula and cook the other side for another 2-3 minutes until it's equally golden. Transfer it to a plate and repeat with remaining tortillas, butter, cheese, and chicken. Let them cool for just 1 minute before serving so the cheese sets slightly.