How to Make It
In a small non-stick skillet, heat 1/2 teaspoon of the oil over medium heat. Season the shrimp with salt and pepper. Add the shrimp to the skillet and cook over moderately high-heat until lightly pink and cooked through, about 3 minutes. Transfer to a plate and let stand.
In the same skillet, heat 2 teaspoons of butter. Add the garlic and jalapeño and cook over moderately low-heat, stirring, until softened, about 1 minute. Add the garlic and chopped chile to the plate of shrimp and lightly toss to combine.
Heat a 1/2 teaspoon of the oil in a large skillet. Place one tortilla in the skillet and scatter with 1/3 cup of the Monterey jack and 1 tablespoon of crumbled cotija cheese. Top half of the shrimp and chile pieces over the cheese onto one side of the quesadilla. Once the cheese has melted lightly all over, gently fold the tortilla in half over the top of the shrimp. Cook over moderately high-heat until crisp and golden on the bottom and cheese is melted, about 2-3 minutes per side. Repeat with the remaining oil to make the second quesadilla. Cut the quesadillas into wedges and serve right away.