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1
Preheat the oven to 400 degrees F.
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2
Season both sides of the green tomato slices with salt and set aside; this will draw out some of the moisture.
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3
Toss the whole canned tomatoes with the vinegar, brown sugar, oil and a large pinch of salt.
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4
Place the whole tomatoes on a parchment-lined baking sheet.
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5
Bake until slightly caramelized and dried out a bit, about 20 minutes.
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6
Set aside.
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7
Set up a standard breading station with three shallow bowls, one with the flour, one with eggs and one with panko.
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8
Season the green tomato slices with black pepper.
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9
Dredge each tomato slice in the flour, shake off the excess, dip in the egg, let excess drip back into the bowl, and then coat in panko.
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10
Set aside on wire rack and repeat with the remaining slices.
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11
Heat 1/2 inch of oil in each of 2 large straight-sided saute pans over medium heat.
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12
Working in batches, fry a few of the tomato slices at a time, turning them once, until golden brown, 4 to 5 minutes a side.
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13
Using tongs, transfer to a paper towel-lined baking sheet.
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14
Repeat with the remaining tomato slices.
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15
Lower the oven temperature to 175 degrees F. Transfer the tomatoes to a wire rack set over a sheet pan.
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16
Place in the oven to keep warm.
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17
Butter the insides of the buns and toast until golden and crispy.
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18
Lay the Burrata on the bottom of the buns, then top with hot green tomatoes, 4 to 5 roasted tomatoes, a spoon of hot giardiniera and some basil.
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19
Close buns, cut each in half and serve with applause.