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1
Defrost the puff pastry for 20-30 minutes on the counter, or overnight in the refrigerator. (Or, make your own.) Preheat the oven to 425u00b0F.
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2
In the small (~5 inches across the bottom) pan that can go into the oven, mix together the tomato paste, pomegranate syrup, and olive oil. Add a large pinch of sugar, a large pinch of salt, and several good grinds of pepper. Thin slightly with water until it's the consistency of maple syrup.
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3
Slice the tomatoes in half through the core and toss them with the syrup in the pan. Arrange them, cut side up in a single layer.
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4
Roll out the puff pastry dough between two pieces of wax paper into a circle about 1 inch larger than your pan.
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5
Transfer the pastry to cover the tomatoes. Tuck the edges around the tomatoes. Cut several short vent in the pastry.
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6
Bake the tarte until the crust is puffed and golden, 25-30 minutes.
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7
Let the tart stand for 5-10 minutes. Run a knife around the pastry to loosen it from the pan. Place a platter on top of the pan and carefully flip the tarte over onto a plate. The tarte may contain a lot of liquid (depending on the juiciness of the tomatoes), so use a towel under the plate.
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8
Chifonnade a few mint leaves and sprinkle them on the tarte. Make sure to eat it before the mint starts to wilt.