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1
Preheat the oven to 375 degrees F. Line a baking sheet with a silicone liner and another baking sheet with a wire rack.
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2
For the eggplant: In a bowl, toss the tomatoes with the balsamic vinegar, olive oil, brown sugar and some salt.
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3
Evenly place the tomatoes on the lined baking sheet.
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4
Place in the oven and roast until slightly caramelized and dried out a bit, 20 to 30 minutes.
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5
Set aside.
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6
Set the eggplant slices on the wire rack (if you don't have a rack you can use a colander set in the sink).
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7
Sprinkle salt on each side of the eggplant and let the salt do the work for 15 to 30 minutes.
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8
Once the salt has released moisture from the eggplant, pat the slices dry with paper towels.
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9
Then sprinkle each side of the eggplant with pepper.
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10
Set up a standard breading station with the flour in one shallow dish, the eggs in another and the panko mixed with the Parmesan in a third dish.
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11
Dredge each eggplant slice in the flour, shake off any excess, dip in the egg, let any excess drip off and then coat in the panko.
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12
Set aside on the wire rack and repeat.
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13
In a large cast-iron skillet, heat 1-inch vegetable oil to 350 degrees F.
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14
Working in small batches, fry the eggplant slices, turning once, until golden brown, 3 to 5 minutes a side.
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15
Using a pair of tongs, transfer back to the wire rack.
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16
Repeat with the remaining eggplant.
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17
Make sure to season the eggplant as it comes out of the oil.
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18
For the sandwich build: Butter and griddle both sides of the buns until golden and crispy (you can toast the buns as well).
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19
Tear the burrata over the bottom buns, then add 2 hot eggplant slices, some roasted tomatoes, a few pickled cherry peppers and some fresh basil leaves on each bun.
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20
Serve to applause.