Step 1Cut off the root end of the leek and cut the white part into 2-inch sections; set aside. Separate the white bulb of the fennel from the branching, leafy tops; set aside some leafy sprigs for garnish if you like. Wash the leek and fennel tops, slice roughly and combine in a saucepan with the water, wine, vinegar, salt, coriander seeds and peppercorns. Slice 1 of the carrots and the celery and add them to the pan. Bring everything to a boil, reduce the heat, and simmer 30 minutes.
Step 2Inspect the scallops; on the shorter side of each you will probably find a small patch of whiter muscle with a denser, more fibrous texture than the rest. Trim these pieces and add to the saucepan.
Step 3Meanwhile, split the leek bottoms lengthwise and cut them into thin strips and rinse them in a deep bowl of water. Quarter the fennel lengthwise, cut the quarters into 2-inch lengths, and cut them into very thin strips. Scrub or peel the carrot and cut it into fine 2-inch thin strips. Check the remaining celery stalk for stringy outer fibers and remove if necessary; cut the celery into fine 2-inch thin strips.
Step 4Strain the vegetable stock and return it to the saucepan. Add the vegetables and simmer until just tender, about 5 minutes. Remove the vegetables with a slotted spoon to warm pasta bowls or deep plates. Taste the broth and correct the seasoning; add the scallops and cook just until heated through, about 30 seconds (you may have to do this in batches depending on the diameter of your pan). Transfer the scallops to the bowls. Pour the broth into a large measuring pitcher and measure 1/2 cup per serving back into the saucepan; reserve the rest for another use. Bring the broth to a boil, then remove from the heat and swirl in the butter. Spoon the sauce over the scallops and vegetables and serve immediately. Add the fennel sprigs for garnish, if you like.