Heat oven to 350 F.
Toss pumpkin, garlic and onions with olive oil. Layer in a large baking dish and drizzle with maple syrup. Bake for 20 minutes.
Stir once, then continue baking for another 20 minutes or until all ingredients are soft and slightly browned. Let cool. If making filling ahead of time, store in an airtight, refrigerated container.
Heat a large nonstick pan to medium-high heat. Place one tortilla in the pan.
Once the tortilla has heated, sprinkle with one sixth of the cheese. Layer a third of the pumpkin mixture over the tortilla.
Layer on spinach, then sprinkle with more cheese. Top with a second tortilla, pressing lightly to compress the quesadilla.
Reduce heat to low, cover pan and heat through until cheese has melted.
When tortilla is lightly brown, flip and brown other side. When done, remove from pan and cut into wedges. Repeat process with remaining ingredients.