Roast carrots at 425°F for 20 minutes, or until the carrots are tender.
While the carrots are cooking, saute the spinach for 2-3 minutes.
Assemble the quesadilla layering the vegetables and goat cheese inside the tortillas in a sandwich arrangement. Then, grill in a skillet for 2 minutes on each side, or until the cheese is melted and the tortilla is brown.