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1
Heat 2 tablespoons oil in a heavy large skillet over medium-low heat.
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2
Add the onions and sugar, and cook until the onions are golden brown, about 20 minutes.
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3
Season the onions, to taste, with salt and pepper; set aside.
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4
Preheat the oven to 250 degrees F.
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5
Sprinkle some Fontina over half of a tortilla.
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6
Arrange some bell peppers and sauteed onions on top of the Fontina.
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7
Sprinkle with chopped parsley and Parmesan.
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8
Sprinkle more Fontina over.
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9
Fold the clean half over the filling to cover and press gently to seal.
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10
Repeat with remaining tortillas evenly dividing the filling ingredients.
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11
Heat 1 tablespoon oil on a heavy large griddle over medium heat.
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12
Working in batches, cook the quesadillas until the cheese melts and the tortillas are golden brown, adding more oil as needed, about 3 minutes per side.
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13
Transfer the quesadillas to baking sheets and keep them warm in the oven while cooking the remaining quesadillas.
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14
Sprinkle the remaining Parmesan over the quesadillas.
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15
Cut each quesadilla into 4 wedges.
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16
Arrange them on a platter.
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17
Garnish the platter with parsley sprigs and serve.
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18
Do-Ahead Tip: The quesadillas can be assembled up to 8 hours ahead.
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19
Arrange them on a baking sheet, cover tightly with plastic wrap, and refrigerate.
