Cut the zucchini in half lengthwise, then into 1/4-inch (5mm) slices. Finely chop the garlic and basil.
Place the corn vertically on a large chopping board. Cut off the corn kernels with a large and sharp knife from the top to bottom. Rotate the ear of corn and repeat until all the kernels have been removed.
Heat the oil in a large frying pan. Cook the zucchini in two batches over high heat until it's browned and tender, but it should still be crunchy, don't overcook it!
Transfer the zucchini into a large bowl.
Add the corn kernels to the pan, cook over high heat for 1-2 minutes or until soft and browned (if using canned corn, you don't have to cook it).
Reduce the heat to medium-low, add the garlic and chili flakes, cook, stirring, for 30 seconds. Transfer the content of the pan to the bowl.
If the zucchini released some moisture or it's too greasy, pat it dry with paper towels. You can't have too much moisture in your filling or it will make the tortilla soggy.
Let the filling cool a little then add shredded cheese and chopped basil. Toss everything together until evenly distributed. Season to taste with salt and pepper.
Spoon some of the filling on one half of a tortilla, fold it over.
Heat a small amount of oil in a large frying pan, place two quesadillas in the pan and cook them over medium heat until golden on both sides and the cheese is melted (move the quesadilla once or twice to make sure it doesn’t stick to the pan).
Transfer quesadillas to a large chopping board, sprinkle with salt on top, cut each quesadilla into 2 or 4 triangles.