Heat 1 tablespoon butter and olive oil in a large skillet over high heat. Add squash, onion and garlic. Sprinkle with salt, pepper, and chili powder. Cook for several minutes, turning gently with a spatula, until squash is golden brown and tender, but not mushy. Transfer to a plate and set aside.
In the same skillet, melt another tablespoon of butter over medium-high heat and add in the kale. Cook it for 3 to 4 minutes, stirring frequently. Add the cooked squash back to the pan & gently toss together.
In a separate skillet, melt additional butter and lightly brown both sides of the tortillas.
Build the quesadillas by adding a layer of cheese topped with a layer of the squash/kale mixture, sprinkled with raw cabbage. Top it off with a second tortilla. Brown each quesadilla on both sides, adding more butter to the pan if necessary. When the cheese is melted, remove each quesadilla from the skillet and cut it into four wedges.
Serve with your favorite sides/toppings.