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1
Preheat the oven to 350.
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2
In a large skillet, heat 2 tablespoons of the olive oil until shimmering.
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3
Add half of the eggplant in a single layer, season with salt and pepper and cook over moderate heat, undisturbed, until browned on the bottom, about 3 minutes.
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4
Stir, cover and cook until the eggplant is tender, about 5 minutes longer.
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5
Scrape the eggplant onto a large plate and repeat with 2 more tablespoons of the olive oil and the remaining eggplant.
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6
Lightly oil a large rimmed nonstick baking sheet.
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7
Sprinkle 1/4 cup of the Parmesan cheese into a 6-inch round on each side of the baking sheet.
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8
Bake for about 3 minutes, until the Parmesan is melted and golden brown.
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9
Let the cheese rounds cool for about 30 seconds to firm up.
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10
With a spatula, carefully lift each round off the baking sheet and drape it over an inverted 4-inch-wide bowl.
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11
Let the cheese stand until cooled and crisp, about 2 minutes.
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12
Repeat with the remaining Parmesan to make 2 more cheese cups.
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13
In a small bowl, whisk the remaining 1/4 cup of olive oil with the vinegar and season with salt and pepper.
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14
In a large bowl, toss the mesclun, scallions, tomatoes and cooked eggplant with the dressing.
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15
Carefully spoon the salad into the Parmesan cups and serve at once.
