Step 1Put the milk, 4 cups of water, the coarse salt, celery root and potatoes in a large pan and bring to a boil over medium heat. Lower the heat and cook at a simmer until the vegetables can be easily pierced with the point of a knife, 20 to 25 minutes. Skim off foam as necessary. Drain the vegetables and return them to the pan.
Step 2Put the pan back over low heat and toss the vegetables just enough to cook off their excess moisture, 1 to 2 minutes. Transfer the vegetables to the work bowl of a food processor. Add the butter and pulse, taking care not to overwork the mixture, just until the puree is smooth and creamy. Season with salt and pepper. Keep the puree warm in the top of a double boiler over simmering water.
Step 1Trim the bottom of each bunch of celery but make certain the stalks remain together. Measure 5 to 6 inches up from the bottom and cut the celery top off at that point (you'll be using the bottom part). Remove and discard the 3 or 4 tough outer stalks. Run a vegetable peeler over the exterior of the outer celery stalks to remove the stringy part of the vegetable, then cut each bunch of celery lengthwise into quarters. Keep close at hand.
Step 2Warm the oil in a large saute pan or skillet over medium heat. Add the carrot, turnip and celery quarters, season with salt and pepper, and cook, without coloring the vegetables, for 3 minutes. Pour in the stock and bring to a boil. Adjust the heat so that the stock simmers steadily and cook the vegetables for about 25 to 30 minutes, or until they can be pierced with the point of a knife. When the vegetables are tender, the liquid should be just about gone, so that you should have tender vegetables lightly glazed with the stock. Remove and discard the carrots and turnips.
Step 3Serve the celery immediately on a large heated platter, spooning the puree on one half and the celery onto the other.