If live, steam snails 1 hour, or until they leave their shells. Remove and rinse.
In a 12 inch to 14 inch saute pan, heat olive oil until smoking. Add onions and garlic and cook over medium heat until soft and lightly brown. Add thyme leaves, snails, wine, olives and tomato and bring to a boil. Lower heat and simmer 30 minutes. Season with salt and pepper and serve.
Saute the onion and garlic in the olive oil over medium heat until translucent, but not brown (about 10 minutes). Add the thyme and carrot and cook 5 minutes more. Add the tomatoes. Bring to a boil, lower the heat to just bubbling, stirring occasionally for 30 minutes. Season with salt to taste. Serve immediately, or set aside for further use. The sauce may be refrigerated for up to one week or frozen for up to 6 months.