In a large saucepan, combine potatoes, celery, onion, and chicken broth. Bring to a boil.
Reduce heat, cover, and simmer for about 10-15 minutes or until vegetables are tender.
Add frozen broccoli and cook for another 5 minutes until tender.
In a separate saucepan, melt butter over medium heat. Stir in flour and cook, stirring constantly, for 1 minute.
Gradually whisk in the milk and cook until slightly thickened, about 3-4 minutes.
Add shredded cheese and stir until melted and smooth.
Combine cheese mixture with the vegetable mixture. Season with salt and pepper to taste.
Simmer on low for another 5 minutes before serving.