Arrange all eight tortillas two by two on a work surface (paired). Sprinkle 1/2 cup of cheese on the four left-hand side tortillas. Top with equal portions of chopped kale and radicchio. Place right-hand tortillas on top of each.
Heat one teaspoon oil in a flat skillet. Place one stuffed quesadilla in pan when hot. Cook one to two minutes (until golden brown) and flip, cooking remaining side for one to two minutes more. Remove and repeat for remaining three quesadillas.
Cut each into quarters and garnish with ingredients such as avocados, tomatoes, and cilantro.