Put the water in the kakugama to boil, add the corn flour and buckwheat flour to rain stirring with a whisk. Cover and cook for 1 hour. Add the butter and salt to season the polenta.
Put the water and vegetables with vinegar and white wine in the kakugama, cook for 20 minutes, and strain into chinoise. Cook the snails in the kakugama with the broth until they are soft (about 2 hours).
Chop the herbs with a knife. Knead all the ingredients together.
Stir the snails with the green butter and chopped truffle. Put the polenta in the dishes, add the snails with butter and garnish with aromatic herbs.