Boil wild rice in rice-cooking water in saucepan. Reduce heat; partly cover and simmer 45 to 60 minutes until tender with many grains split. Drain well.
Heat oven to 425°F. Toss celery root with oil and salt on sheet pan; roast 25 to 30 minutes, turning once, until tender with browned edges.
Melt butter in soup pot over medium. Cook mushrooms and onion 7 to 8 minutes until mushrooms brown and onion softens.
Add cider; simmer 2 minutes. Add broth, thyme, ham, and pepper; gently simmer 10 minutes.
Fold in drained rice and roasted celery root; simmer 5 minutes until hot and ham 165°F. Remove thyme stems; stir in mustard.
Divide among six bowls, distributing rice, vegetables, and ham evenly.