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Taste the watermelon. If it is not fully flavorful and sweet, stop now.
Cut off the rind and remove seeds from a generous cup of watermelon and cut it into small dice. Reserve and chill. This will both finish and garnish the soup.
Crush and purée remaining watermelon — seeds and rind removed — with a hand tool as best you can. Pass it through a coarse sieve or colander, pressing the pulp through. The goal is to separate and discard any remaining seeds or bits of rind. There should be around 7 cups of pulp and juice.
Put juice and pulp into a blender or food processor with a steel blade, working in batches if necessary. Add ice, almonds, and garlic and blend until smooth.
Add bread, vinegar, and salt, plus pepper to taste. Blend while adding the olive oil in a slow stream.
Transfer to a large serving bowl or to small individual bowls. Add diced melon and serve. Fresh mint leaves are a great garnish.
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