In a small bowl, whisk together the mayonnaise, hot sauce, lime juice, and chile powder. Add the corn and cotija cheese. Stir to combine and set aside.
Warm a large skillet over medium-high heat. Lightly butter one side of each tortilla with about ½ a teaspoon of butter.
Place one tortilla buttered side down in the hot pan. Top with half of the Monterey Jack cheese. Spread the corn mixture over the cheese. Top with the remaining cheese. Sprinkle with cilantro and top with the second tortilla.
When the cheese has begun to melt and the bottom tortilla is browning slightly, flip the quesadilla over to cook the second side. Continue to cook until the cheese has melted and both tortillas are crisp around the edges.
Using a spatula, transfer the quesadilla to a cutting board and cut it into wedges while it is hot. Serve warm.