Position an oven rack in the center of the oven and preheat it to 425 degrees F. Line 2 rimmed baking sheets with parchment and set aside.
Put the squash in a medium bowl and add 3 tablespoons of the oil, 2 teaspoons of salt and a few grinds of pepper. Mix until the squash is well coated. Divide and spread the squash out in a single layer between the 2 prepared baking sheets. Roast until tender, about 30 minutes.
Add the remaining 2 teaspoons of oil to a medium skillet over medium-high heat. Add the shallot and cook, stirring, until brown and soft, about 3 minutes. Raise the heat to high and add the spinach with whatever water clings to the leaves and sprinkle with salt and pepper. Stir while incorporating any browned bits from the bottom of the skillet. Cover the skillet and cook until wilted, about 1 minute.
Lay a tortilla on a work surface and top evenly with 1/2 cup mozzarella. Add 1/4 of the butternut squash and 1/4 of the spinach. Fold tortilla in half to enclose fillings. Repeat with remaining tortillas and ingredients.
Melt 1/2 tablespoon butter in a large non-stick or cast-iron skillet over medium heat. Cook the quesadilla, flipping once, until the cheese is melted and the quesadilla is golden brown, about 3 minutes per side. Remove to a cutting board and repeat with the remaining quesadillas.
Cut into triangles and serve with guacamole, scallions, salsa and sour cream.
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