In a 5- to 6-quart pan over medium-high heat, bring peas and 7 cups water to a boil. Add ham bone, celery, onion, carrots, bay leaf, thyme, and 1/2 teaspoon each salt and pepper; return to a boil.
Lower heat to maintain a simmer, cover, and cook, stirring occasionally, until peas have broken down and soup has thickened, about 2 1/2 hours.
Remove ham bone and bay leaf. When cool enough to handle, pull any meat remaining on ham bone into shreds and return to soup (discard bay leaf and ham bone). If soup is too thick, thin with water to desired consistency. Add more salt and pepper to taste.