Place everything but a few tomatoes and the coarse salt into a blender and purée, gradually increasing the speed until soup is smooth. Adjust with more milk or broth if soup is too thick.
Serve immediately, or chill for an hour, topped with a few thin slices of tomato and a sprinkling of coarse salt. To serve as an amuse bouche, pour into shot glasses, or other small cordial glassware and top with a brunoise (tiny dice) of tomato and salt.
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