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1
In a heavy kettle cook the onions with the rosemary, the thyme, and salt and pepper to taste in the butter and the oil, covered, over moderately low heat, stirring occasionally, for 20 to 30 minutes, or until they are soft but not golden, add the sugar, and cook the mixture, uncovered, stirring, for 5 to 10 minutes, or until the excess liquid is evaporated.
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2
Transfer the onion mixture to a fine sieve and let it drain for 10 minutes.
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3
The onion mixture may be made 1 day in advance and kept covered and chilled.
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4
Roll each sheet of puff pastry lightly on a floured surface into an 11- by 10-inch rectangle and transfer and rectangles to a baking sheet.
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5
Brush a 1-inch border around the edges of each rectangle with some of the egg wash and fold in the edges on all sides to form a 1/2-inch border, mitering the corners if desired.
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6
Brush the folded borders with the remaining egg wash and with the back of a knife score them in a crosshatch pattern.
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7
Sprinkle 4 tablespoons of the Parmesan evenly over the rectangles, divide the onion mixture between them, spreading it evenly, and arrange the anchovy strips and the olives decoratively on top.
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8
Sprinkle the remaining 2 tablespoons Parmesan evenly over the tarts and bake the tarts in the upper third of a preheated 400F.
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9
oven for 15 to 20 minutes, or until the pastry is puffed and golden.
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10
The tarts may be made 1 day in advance, kept covered loosely at room temperature, and reheated.
