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Heat oven to 425°F.
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Heat oil in a large sauté pan over medium-high heat. Add onions, 1-1/2 teaspoons of the salt and 1/2 teaspoon of the pepper. Sauté onions until translucent, about 10 minutes.
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Lower heat to medium; cook onions until golden brown and caramelized, about 15 minutes. Remove from heat; reserve.
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Sprinkle flour on a work area; roll out puff pastry using more flour as necessary to keep pastry from sticking. Roll each sheet pastry into a rectangle 11x13-inches.
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Place the sheets on a large parchment-lined sheet pan. Fold the edges of each sheet 1/2-inch over the pastry to form a rim. Press the edges with the tines of a fork.
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Place the sheets on a large parchment-lined sheet pan. Fold the edges of each sheet 1/2-inch over the pastry to form a rim. Press the edges with the tines of a fork.
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Bake the pissaladiere 20 to 25 minutes or until the pastry is crisp and brown on the bottom.
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Cut each into quarters and serve hot or at room temperature.