Cut the delicata squash in half, scoop out seeds, and slice into ¼ inch thick slices.
Combine the squash, peppers, and onions in a large bowl. Add the oil, cumin, paprika, chipotle, ancho, salt, and cayenne, and mix until vegetables are evenly coated with the oil and spices.
Spread vegetables in a single layer on a baking sheet and bake at 400 degrees until squash is crispy and tender, about 25-30 minutes.
To assemble quesadillas, place 4 tortillas down and top each with 2 Tbsp of grated cheese. Divide roasted vegetables evenly between the tortillas and top with the remaining cheese, followed by the remaining 4 tortillas.
Heat a skillet over medium heat. Once hot, place the quesadillas on the skillet, cooking until bottom tortilla is golden brown. Carefully flip, and continue cooking until the other side is golden brown.
Cut quesadillas into quarters and serve! Salsa, sour, cream, avocado, lime, and/or hot sauce highly recommended as an accompaniment.