Take the snails out of the can, wash under hot running water, drain. Pour the wine into a deep dish, add the sliced carrot, thyme, salt, pepper and snails. Marinate for at least 1/2 hour. Detach the mushroom caps, coat lightly with oil, salt, pepper, put into an ovenproof dish and bake for a few minutes under the grill of the oven, keeping an eye on them. Chop the mushroom stems with the shallots, garlic and parsley. Add to this stuffing the snails, drained and cut into small pieces, the bread crumbs, salt and pepper, moisten with a little white wine from the marinade. Fill the mushrooms with this stuffing, top each with a tablespoon of butter and bake in a hot oven (350F) for 10 to 15 minutes.
