Before discussing how to improve a quesadilla, I think it's important to first talk about pizza.
Look at this picture of a cheese pizza that I found online:
Looks good right? Sure does. But what if I was to ask you why it looks good? What about this pizza makes you think it'd taste delicious? My guess is that your answer would have something to do with all those gooey, melted strands of cheese. Right?
But I'd argue that while those gooey, melted strands of cheese are indeed a glorious, they're not actually contributing much when it comes to the flavor of the pizza. Rather, they're playing a crucial textural role—and though texture works closely in conjunction with flavor, it isn't flavor exactly. What is doing the heavy lifting re: the flavor we most associate with a great cheese pizza, are all those brown spots of cheese. Those are all the spots of cheese that have caramelized, creating that rich, toasted flavor you love when you bite into your favorite slice of pizza.
A classic quesadilla has the cook melt the cheese inside of a tortilla placed on a hot griddle. The tortilla transmits the griddle's heat evenly, the cheese melts, everyone is happy (and in the case of this huitlacoche quesadilla I ate in Mexico City last year, very, very happy). But no part of this process allows the cheese to get hot enough to create those rich, caramelized flavors. It never occurred to me to try to add, we'll call it, "pizza cheese" flavor to a quesadilla before, but then, on that same trip to Mexico, I saw something that changed my mind. While waiting for a late lunch of tacos arabes in Puebla, I watch the cook take take the cheese destined for my taco and scatter it directly on the griddle. She then placed a warm tortilla on top of that, waited about 45 seconds, and scooped the entire thing up. One side of the cheese was browned and delicious, the other side gooey and fused to the tortilla. It's was brilliant. And that simple technique has forever improved the quesadillas I make at home.
Here how to do it.
After either procuring or producing tortillas, it's time to grate some cheese. If you want to keep it authentic, go with a nice Oaxacan melting cheese, which is essentially a Mexican mozzarella. Most days though I use a combination of pepper jack (which, as far as comfort and classiness is concerned, is like the sweatpants of cheese), medium cheddar, and low-moisture whole milk mozzarella.
Heat a griddle or non-stick pan over medium heat, then add the pepper-jack and cheddar in little, tortilla-sized circles.
Immediately top with pre-warmed tortillas, pressing lightly to adhere to the melting cheese. It'll take only 30-45 seconds to caramelize nicely. This is something you'll be able to smell happening.
Use a spatula to free the cheese from the pan and invert it.
Here I add just a little extra mozzarella to bring a melty, stringy texture to the game. Fold the tortillas in half and cook on both sides until the cheese is melted. Feel free to add a little oil to the pan if you want to crisp up the outside of the tortilla.
And there it is. An insanely delicious, caramelized cheese quesadilla.
Cover this with salsa, and dig in.
OR, make some rajas for the filling.
Grill some onions, roast a poblano or two, and then chop them up with cilantro, salt, and fresh lime juice.
There is nothing in the world worth learning that you can't learn from pizza and a Mexican cook.