If you are beginning with freshly gathered snails you should keep them in a sealed basket in the dark for 20 days, during which they'll fast, and thus loose the wild earthy flavor they have when freshly caught. If you're buying them, find out if the person selling them has done this.
Once they've fasted they have to be prepared. Put them in a tub of cold water and leave them there for at least three hours. Discard any that rise to the surface because they are already dead. Don rubber gloves, transfer the snails to a large pot, douse them with the vinegar, sprinkle them with the salt, and stir them about for a half hour, during which they will expel a great deal of slime.
Rinse them in cold running water for 20 minutes to remove the slime, boil them in unsalted water for a half hour, and then shell them, cutting away and discarding the black innermost part of their bodies, which contains the intestines.
If you would rather avoid this lengthy, unpleasant preparatory phase, buy canned snails that have been cooked and shelled.
Once your snails are ready, mince the herbs, the garlic, the onion, and the celery, and heat the oil in a broad high-sided skillet. Add the herb mixture and the snails, and sauté until the onion begins to turn gold. Add the white wine and cook until it evaporates, then the tomato and a couple of cups of hot water. Cover and simmer for a couple of hours over a low flame. If need be add a little more water towards the end of the cooking; the sauce should be thick but still flow.
While the snails are cooking prepare the polenta: Bring three quarts (liters) of water to a boil and add the corn meal in a thin stream, stirring with a wire whisk or a spoon to keep lumps from forming. Continue to cook, stirring constantly, for about 70 minutes, or until the polenta is firm. Pour it out onto a board, cut it into slices using a taut string, and serve it with the snail sauce.
The authors note that they call for mountain snails because they live far from pollution and over cultivation that has eliminated hedges and ditches, thus destroying snail habitats. They also say that until quite recently farmers would go out into the brush after a heavy summer rain with boots and gloves, to gather the snails who came out from their hiding places to enjoy the cool and damp, and observe that snails are an excellent bet for listless lovers: Snails, according to Voltaire, are certainly the species best favored by nature. They're blessed with twin pleasure organs and their ecstasy lasts from three to four hours. Not much by comparison with eternity, but a very long time compared to you or me. Much better, they conclude, than hot pepper or oysters!
The wine? I'd suggest a white, for example a Verdicchio.
Note: according to Giuliano Bugialli, Mentuccia is the variety of thyme known as Nipitella in Tuscany, which adds that special secret something to many porcino recipes.
