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1
Prepare an ice-water bath by filling a large bowl with ice and water.
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2
Line a plate with paper towels.
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3
To cook the corn, bring a large pot of salted water to a rolling boil over high heat.
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4
Add the corn and cook until tender, 2 to 3 minutes.
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5
Remove with tongs to the ice water to cool, then transfer to the towel-lined plate to drain.
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6
To cook the black-eyed peas, add them to the pot and simmer until tender but not mushy, about 20 minutes.
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7
(Taste one and see how tender it is; the cooking time will depend on their freshness.)
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8
Meanwhile, cut the corn kernels from the cobs and place in a large bowl.
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9
Add the tomatoes, onion, and garlic.
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10
When the peas are tender, drain them in a colander, then shock under cold running water to stop the cooking.
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11
Once the peas are completely cool, drain very well, shaking to remove all the moisture, and add to the corn mixture, along with the basil.
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12
Set aside.
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13
To make the dressing, whisk together the vinegar and mustard in a bowl.
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14
Add the oil in a slow steady stream, whisking constantly, until the dressing is creamy and emulsified.
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15
Season the dressing with salt and pepper.
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16
To serve, drizzle over a little of the salad dressing.
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17
Toss to coat, adding more if needed.
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18
Taste and adjust for seasoning with salt and pepper.
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19
Serve immediately.