Saute celery, onion, and garlic in the 2 tablespoon butter. Add potatoes and water, and simmer for 30 minutes. Add clam base, a pinch of thyme, salt, pepper, and hot water. Simmer for 15 minutes and add clams and carrot. Simmer 15 minutes and add half and half and water. Heat through until simmer. Meanwhile make a roux out of the 1/2 cup butter and the 1/2 cup flour make sure that the flour cooks through before adding this to the simmering soup.