In a large soup pot, boil vegetables in water, salt, and bouillon till tender, about 10 minutes. Add pepper and ham.
In a small saucepan, melt the butter over medium heat. Whisk in the flour. Slowly whisk in the milk and keep whisking till smooth. Cook over medium heat till bubbly, stirring constantly. Boil for at least one minute to get rid of the flour taste.
Pour white sauce into the vegetable mixture and stir till smooth. Add the dill if desired. Serve with grated cheddar cheese.