Place the garlic in a large mortar and pestle and mash well. Add the egg yolks and mash. While mashing, very slowly add the olive oil, drop by drop, to create an emulsion. When the mixture is thick and the oil is all added, season, to taste, with salt and pepper.
Soak the cod in water in the refrigerator for 3 days, changing the water 2 to 4 times a day. Drain well and cut into 2-ounce pieces. Bring a large pot of water to a boil. Add the bay leaf and lower to a simmer. Poach the cod in the water until just cooked, about 4 to 6 minutes. Drain and set aside to cool.
Place the cod, eggs, carrots, cauliflower, string beans, potatoes, and snails on a large platter. Drizzle with the aioli. Serve remaining aioli in a bowl.