In a large saucepan, combine broccoli, celery, onion, and broth; bring to boiling. Reduce heat, cover, cook until vegetables are tender.
In a bowl, combine milk, cornstarch, thyme, and salt/pepper to taste; add to cooked vegetables. Cook, stirring constantly, until thickened and bubble.
Remove from heat and let stand
Add cheese to pan; stir until cheese melts