Combine the chili powder, cumin, garlic powder, cayenne pepper, and salt in a small bowl. Coat the boneless skinless chicken thighs (or breasts) evenly on all sides. This spice blend is what makes the difference between a bland quesadilla and one that actually tastes like a restaurant made it.
Heat 2 tablespoons olive oil in a skillet over medium-high heat. Add the seasoned chicken and cook 5-6 minutes per side until cooked through and nicely charred on the edges. Remove and let rest 5 minutes, then slice or chop into bite-sized pieces. Squeeze fresh lime juice over the top.
In the same skillet, add a touch more oil if needed and cook the onion and jalapeño over medium heat for 4-5 minutes until softened and lightly caramelized. Remove and set aside.
Lay 4 large flour tortillas flat. Cover one half each with a generous layer of the shredded cheeses, then top with the chicken, onion and jalapeño mixture, then a little more cheese. Fold the tortilla over in half. The cheese on both sides acts as the glue that holds everything together when you cut it.
Melt 2 tablespoons butter (for the tortillas) in a cast iron or non-stick skillet over medium heat (Use a large griddle for real-deal restaurant results). Add the quesadilla and cook 2-3 minutes per side, pressing down lightly with a spatula, until deeply golden and the cheese is fully melted. The butter is key for that golden, slightly crispy exterior that plain oil doesn't achieve.
Slide onto a cutting board and cut into wedges while hot, or serve whole if desired. Garnish with fresh chopped cilantro. Serve immediately with sour cream, guacamole, salsa, or a squeeze of extra lime, with refried beans and Mexican rice on the side. Don't wait! Quesadillas are best the moment they come off the heat.