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1
In a bowl, toss the chicken thighs with 2 tablespoons of the olive oil, the rosemary, garlic and a generous pinch of salt.
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2
Cover and let the chicken stand at room temperature for 30 minutes or refrigerate for 4 hours or overnight.
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3
Meanwhile, in a large, deep skillet, melt the butter in the remaining 1 tablespoon of olive oil.
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4
Add the sliced onions, thyme, vinegar, sugar and a generous pinch of pepper.
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5
Cook over moderately low heat, stirring occasionally, until the onions are softened, about 30 minutes; add a few tablespoons of water from time to time to keep the onions moist.
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6
Light a grill and preheat the oven to 500.
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7
Season the chicken with salt and pepper and grill over moderately high heat, turning, until lightly charred and cooked through, about 15 minutes.
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8
Let the chicken cool, then pull the meat from the bones and tear into shreds.
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9
Arrange 6 tortillas on 2 large baking sheets.
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10
Spoon the onions onto the tortillas and top with the shredded chicken and blue cheese.
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11
Cover with the remaining tortillas, pressing to flatten slightly.
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12
Bake for about 6 minutes, until the quesadillas are golden and toasted.
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13
Transfer the quesadillas to plates and serve right away.
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14
*The unbaked quesadillas can be tightly wrapped in plastic and refrigerated overnight.
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15
**WINE SELECTION:One great region for Zinfandel is Sonoma's warm Dry Creek Valley, as evidenced by wines like the plummy 2004 Ferrari-Carano and the chocolate-inflected 2005 Dashe Dry Creek Valley.
