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1
Preheat the grill or broiler.
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2
Mound the flour and salt in the center of a cutting board.
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3
Using a pastry cutter, cut the butter into the flour until the mixture resembles coarse crumbs.
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4
Mix in the egg and cold water and work the dough just enough so that it comes together.
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5
Wrap in plastic and refrigerate 30 minutes.
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6
Brush the eggplant slices with olive oil and grill on both sides until marked and crispy, about 3 minutes per side.
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7
Set aside.
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8
Meanwhile, in a 12 to 14-inch skillet, heat the olive oil over high heat until just smoking.
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9
Add the garlic and onion and saute over high heat until light golden brown.
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10
Add the mint, thyme, oregano and salt and pepper to taste and cook 5 minutes more.
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11
Stir in the tomato puree, bring to a boil, simmer until very thick and stew like and remove from heat.
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12
Preheat the oven to 350 degrees F. Roll the dough out to an even 1/8-inch thickness and fit it into a 10-inch tart pan.
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13
Blind bake the pastry shell for 20 minutes, until golden brown, then remove from oven and allow to cool.
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14
Layer the eggplant slices and tomato sauce mixture in the tart shell, alternating layers and ending with a layer of eggplant.
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15
Cut the slices if necessary to fit the pie shell.
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16
Top with abundant grated cheese and bake in the oven 20 minutes, until the cheese is browned and the sauce is bubbling.
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17
Let cool 15 minutes, then slice and serve.