Heat the water to boiling in a large pot. Add the bouillon cubes and dissolve. Cut the onion into thin slices, then quarter the slices and add to the broth. Add salt and pepper.
Bring the mixtue back to a boil. Turn down the heat and simmer uncovered for 1 hour while stirring. Sifft the flour into the soup and continue to stir until smooth. Be careful when you stir so you do not tear the onions.
As the soup continues to cook any lumps should disslove after 30 minutes or additional simmering. Add the cream and 1 cup of cheddar cheese,continue to simmer the soup for another 5 to 10 minutes. Serve the soup hot after sprinkling a tablespoon of each of the cheeses on top.