Bring broth and liquid from the potatoes to boiling in a large saucepan. Add mixed vegetables, onion and thyme. Return to boiling. Reduce heat to medium. Cover and cook 5 minutes or until onions are just tender.
Meanwhile, finely chop ham and potatoes.
Add ham, potatoes, half-and-half and pepper to saucepan. Cover; simmer to heat through, 2 minutes.