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1
Preheat the oven to 400F.
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2
Line a baking sheet with parchment paper.
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3
Cut each squash half crosswise into 1/4 inch slices, resembling halfmoons.
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4
In a large bowl, toss the squash with the olive oil, and sprinkle with salt and pepper to taste.
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5
Place the squash on the prepared baking sheet and roast for 20 to 25 minutes, turning the pieces over halfway through, or until the squash feels soft when pierced with a fork and the slices are slightly caramelized.
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6
Set aside to cool slightly.
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7
In a small bowl, mash the butter and Parmesan together.
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8
To assemble: Spread the Parmesan butter on one side of each tortilla and place them on your work surface, buttered side down.
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9
Place 6 slices of squash on the bottom half of each tortilla, followed by the Gruyere, blue cheese, and sage.
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10
Fold the tortillas in half to enclose the filling, forming a half-moon.
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11
(You may have extra squash slices; save for another use or enjoy as a snack.)
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12
Stovetop method: Heat a large nonstick skillet over medium heat for 2 minutes.
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13
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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14
Watch carefully, as the Parmesan butter can burn easily.
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15
Uncover, and turn the quesadillas with a spatula.
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16
Cook for about 1 minute, or until the undersides are golden brown and the cheese has melted completely.
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17
Repeat with the remaining 2 quesadillas.
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18
Cut the quesadillas in half, and serve immediately.
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19
Sandwich maker method: Preheat the sandwich maker (if your machine has adjustable heat, set it to medium).
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20
Follow directions for quesadilla assembly.
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21
Cook for 3 to 4 minutes or until the cheese has melted completely.
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22
Watch carefully, as the Parmesan butter can burn easily.
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23
Unless you have a large sandwich maker, you will have to cook the quesadillas in batches.
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24
Gas grill method: Brush the grill rack with oil and preheat the grill to medium.
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25
Follow directions for quesadilla assembly.
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26
Put the quesadillas on the grill and follow directions for the stovetop method.
