Coarsely chop the almonds and set aside. Chop or tear the bread into large pieces. Put in a bowl and cover with the milk. Allow to soak until it has softened, about 5 minutes. Blend the almonds, garlic, ½ cup (120 mL) of olive oil, vinegar, 4 cups (950 mL) of water, ¾ of the cucumber, and ¾ cup (180 mL) grapes in a food processor or blender in batches until smooth. Add the bread and milk in 3 parts, blending each time until the bread is emulsified. Taste and add salt and pepper.
Press through a sieve and discard the solids. Blend in the extra ¼ cup (60 mL) olive oil and up to 1 cup (240 mL) of water if necessary for flavor or consistency. Taste again and season with more salt and pepper if needed.
Refrigerate until completely chilled. Chop the remaining peeled and seeded cucumber into ¼ -inch (.6-cm) dice and cut the remaining grapes in half. Chill those too.
Spoon 2 to 3 Tbsp. (30 to 45 mL) of the diced cucumber and the grapes into each bowl or thin, tall glass. Pour the soup over and garnish with a tiny sprig of mint. Serve immediately.