For the snails, boil the peeled potatoes in salted water until soft and let cool slightly. Using a small knife, cut straight down two sides and cut the potato into an oval shape.
Using a Parisienne or round cutter, cut a small hollow in each potato for a snail. Cover with foil and keep warm.
Finely dice the peeled shallots, carrot and celery. Sauté in a little olive oil and deglaze with Pernod, Noilly Prat and white wine. Simmer over low heat until soft.
Mix in crème fraîche, stir in cold butter, but do not boil anymore and season with freshly ground salt and pepper.
Heat the snails in this broth and place one in each potato.
Cover the potatoes with some vegetable sauce (keep the rest warm) and sprinkle with freshly grated Parmesan.
Place in a baking dish and bake briefly in the oven preheated to 220 °C with strong top heat.
Arrange six potatoes on each plate and garnish with the remaining sauce and freshly chopped parsley.