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1
Preheat oven to 400; line a baking sheet with parchment paper.
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2
Cut each squash half crosswise into 1/4-inch slices.
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3
In a big bowl, toss the squash with the olive oil; sprinkle with salt and pepper.
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4
Place the squash on the prepared baking sheet; roast for 20-25 minutes, turning pieces over halfway through, or until the squash feels soft when pierced with a fork and the slices are slightly caramelized; set aside to cool slightly.
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5
In a small bowl, mash the butter and parmesan together.
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6
Spread the parmesan butter on 1 side of each tortilla and place them on a work surface, buttered side down.
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7
Place 6 slices of squash on the bottom half of each tortilla, followed by the Gruyere, blue cheese, and sage; fold the tortillas in half to enclose the filling.
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8
Heat a large nonstick skillet over medium heat for 2 minutes; place 2 of the quesadillas in the skillet, cover, and cook for 2 minutes or until the undersides are golden brown and the cheese has begun to melt.
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9
Watch carefully, as the Parmesan butter can burn easily.
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10
Uncover, and turn the quesadillas with a spatula; cook for about 1 minute, or until the undersides are golden brown and the cheese has melted completely.
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11
Repeat with the remaining 2 quesadillas; cut in half and serve immediately.