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1
Position an oven rack about 4 inches below the broiler and heat the broiler on high. Arrange the prosciutto in a single layer on a small baking sheet and broil until it begins to curl, 1 to 2 minutes. Flip the prosciutto and broil until it appears dry-crisp and has curled a bit more, about 1 minute. Let cool, then finely chop or crumble by hand; set aside.
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2
Slice the kernels off the corn cobs for a total of 3 cups corn. Reserve the cobs.
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3
In a medium Dutch oven over medium heat, melt the butter. Add the onion and cook until softened and slightly golden, 5 to 7 minutes. Season with a generous pinch of salt.
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4
Add 4 cups of water, the broth, potatoes, 1-1/2 cups of the corn, the cobs, and 2 tsp. salt. Bring to a boil. Reduce the heat to medium low and simmer until the potatoes are tender, 10 to 15 minutes. Remove from the heat and discard the cobs.
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5
Working in batches, carefully puree the soup in a blender, transferring each batch to a large heat-proof bowl or large liquid measuring cup.
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6
Pour the pureed soup back into the pot. Add the remaining 1-1/2 cups corn and bring to a boil over medium-high heat. Reduce heat to medium low and simmer, stirring occasionally, until the corn kernels are tender, 3 to 5 minutes. Season to taste with salt and pepper. Garnish each serving with the crisped prosciutto and basil.
