Combine the undrained oysters and cold water in a stockpot. Melt the butter in a skillet and add the onions and garlic. Cook until the onions are light brown, stirring frequently. Add the flour and stir until combined.
Add the onion mixture, bay leaves, Tabasco sauce, thyme, pepper, and salt to the stockpot. Simmer, tightly covered, over low heat for 3 hours. Remove from the heat and discard the bay leaves. Stir in the half and half and ladle into soup bowls.