Bring wild rice and rice-cooking water to a boil in a saucepan. Reduce heat, partly cover and simmer for 45 to 60 minutes until the grains are tender and many have split open; drain well.
Heat oven to 425°F. Toss celery root with olive oil and salt on a sheet pan and roast for 25 to 30 minutes, turning once, until tender and browned at the edges.
Melt butter in a soup pot over medium heat. Cook mushrooms and onion for 7 to 8 minutes until the mushrooms brown and the onion softens.
Add cider and simmer for 2 minutes, then add broth, thyme, ham and pepper. Simmer gently for 10 minutes.
Fold in drained wild rice and roasted celery root and simmer for 5 minutes until everything is hot and ham reaches 165°F. Remove thyme stems and stir in mustard.
Divide among six bowls with wild rice, vegetables and ham in each serving.