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Remove the husks from the corn. Bring a large pot of salted water to a rolling boil and drop in the corn. Blanch until tender but al dente. 8 to 10 minutes. Remove with a slotted spoon and set aside.
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In the same water, boil the potatoes for about 20 minutes, until firm and about three quarters of the way cooked. They should be piercable but firm enough to cut into thick slices without falling apart. Remove from the water with a slotted spoon and submerge into an ice-water bath. When the potatoes are cool enough to handle, remove, peel, and cut each potato into four
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thick oval lengthwise slices.
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While the potatoes are blanching, heat the grill to medium-hot.
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Gather the potatoes with the corn and olive oil and set them near the grill.
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Brush the corn and potato slices with olive oil. season lightly with salt. and grill until the potatoes are tender but firm and lined with grill marks and the corn is lightly charred, about 5 minutes. Remove.
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Let the corn cool slightly, then using a sharp paring knife, cut off the kernels into a serving bowl. Cut the potato slices into 1 1/2-inch cubes. Don't worry if the potatoes fall apart slightly -- add every last bit of them to the serving bowl. Add the onion. Tomatoes, basil, parsley, and purslane. Peel and cut the hard-boiled eggs into quarters and add to the top of the salad.
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Whisk together the remaining olive oil and the vinegar and season with salt and pepper. Pour over the salad. Toss gently and serve.