Cook cucumbers in a 4- to 5-quart pot of boiling salted water, uncovered, just until water returns to a boil, about 1 minute, then immediately drain in a colander and transfer to a bowl of ice and cold water to stop cooking.
Drain cucumbers well, then purée in 2 batches in a blender until as smooth as possible, about 1 minute, transferring to a bowl.
Peel potato and cut into 1/2-inch cubes. Cook onion, carrot, celery, garlic, bay leaf, and thyme in butter in a 2-quart heavy saucepan over moderate heat, stirring occasionally, until vegetables are softened, about 3 minutes.
Add potato, 4 cups water, pepper, and 1/2 teaspoon salt and simmer, partially covered, until potato is very tender, about 15 minutes. Discard bay leaf and thyme.
Purée mixture in batches in blender until very smooth, about 1 minute (use caution when blending hot liquids), transferring to a large bowl. Chill, uncovered, until completely cool, about 30 minutes.
Stir cucumber purée into potato purée and force soup through a fine-mesh sieve into a large bowl, pressing hard on and then discarding solids.
Stir remaining teaspoon salt into soup, then reheat in a bowl in a microwave or in a saucepan on stovetop over low heat (microwaving is best because it preserves the soup's bright green color). Put 1 mousseline in each of 10 shallow soup bowls and pour warm soup around each.
Soup can be made 2 days ahead and chilled, covered.
