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1
In a medium shallow bowl, combine the cornmeal, salt, black pepper, and cayenne pepper; set aside.
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2
In another shallow bowl, whisk together the buttermilk, eggs, and lime juice (the mixture may appear curdled); set aside.
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3
In a large cast-iron or heavy skillet, pour oil to a depth of 1/2 inch; heat until a deep-fry thermometer measures 375F.
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4
Meanwhile, working in batches, dip the tomatoes in the buttermilk mixture, then in the cornmeal mixture.
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5
Set aside on a large plate; repeat with the remaining tomatoes.
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6
Fry the tomatoes, working in batches, until golden brown, about 1 minute on each side.
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7
Drain on a paper-towellined plate.
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8
Season with salt while hot.
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9
Serve warm with basil-lime mayonnaise.
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10
In a food processor, pulse the egg with the salt and pepper until foamy and pale, about 1 1/2 minutes.
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11
With the machine running, add the oil through the feed tube, 1 drop at a time, until the mixture starts to thicken (do not stop the machine at this point, or the mayonnaise may not come together).
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12
Add the remaining oil in a slow, steady stream.
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13
When all the oil has been incorporated, slowly add the lime juice, mixing until combined.
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14
Add the basil; pulse until combined.
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15
Let chill before serving.
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16
Fresh mayonnaise can be refrigerated in an airtight container up to 5 days.
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17
Raw eggs should not be used in food prepared for pregnant women, babies, young children, the elderly, or anyone whose health is compromised.