Split Pea Soup

1 pound split peas
3 quarts water
1 tsp. salt
1/2 tsp. pepper
1 cup sliced carrots
1 cup sliced celery
1 medium onion, chopped
1 bay leaf
1/4 tsp. dried thyme
1/2 cup chopped ham (optional)
1 cup half-&-half

Rinse peas in a colander. Combine all ingredients except half-&-half in a large stockpot. Bring to a boil. Lower heat and simmer 2 1/2 to 3 hours. Add half-&-half and heat through.