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1
Heat 1/4 cup oil in heavy large nonstick skillet over medium-high heat.
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2
Working in batches, add eggplant to oil and saute until light brown, turning once and adding up to 2 tablespoons more oil as necessary, about 1 minute per side.
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3
Transfer eggplant to paper-towel-lined plate to drain.
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4
Sprinkle with salt and pepper.
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5
Cook tomatoes in boiling water for 1 1/2 minutes.
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6
Peel, seed, and chop into 1/2-inch pieces.
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7
Heat 1 tablespoon olive oil in heavy small saucepan over medium-high heat.
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8
Add onion, carrot, and half of garlic; saute 5 minutes.
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9
Add tomato, thyme, 2 tablespoons water, and bay leaf; reduce heat to low and simmer until slightly thickened, about 15 minutes.
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10
Discard bay leaf.
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11
Season tomato mixture to taste with salt and pepper.
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12
Place basil, 3 tablespoons oil, pine nuts, 1 tablespoon Parmesan cheese, and remaining half of garlic in processor; puree.
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13
Set pesto aside.
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14
Preheat oven to 350F.
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15
Place 4 individual gratin dishes (about 7x4 3/4 inches) on rimmed baking sheet.
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16
Place 2 slices eggplant in 1 prepared dish.
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17
Top with 1/4 of tomato mixture, 3 slices mozzarella cheese, 2 tablespoons pesto, and 1/4 cup Parmesan cheese.
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18
Repeat layering of remaining ingredients in 3 gratin dishes.
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19
Bake until heated through, about 8 minutes.
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20
Preheat broiler.
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21
Broil until cheese bubbles, about 3 minutes.
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22
Serve hot.