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1
In a small heavy saucepan cook the leek with salt and pepper to taste in 1 tablespoon of the oil over moderate heat, stirring, until it is softened, add the garlic, the potato, drained, and the broth, and simmer the mixture, covered, for 8 to 10 minutes, or until the potato is very soft.
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2
Stir in the arugula, simmer the mixture, covered, for 1 minute, and in a blender puree it in batches for 2 minutes, or until it is completely smooth.
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3
Transfer the puree to a metal bowl set in a larger bowl of ice and cold water, stir in the half-and half, and chill the soup, stirring occasionally, for 10 minutes, or until it is cold.
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4
While the soup is chilling, in small heavy skillet cook the bread cubes in the remaining 1 tablespoon over moderate heat, stirring, until they are browned, transfer the croutons to paper towels, and season them with salt.
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5
Divide the soup between 2 bowls and top it with the croutons and the tomato.