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© Meredith Corporation. All rights reserved. Used with permission.
Heat oil in a large pot over medium heat. Add onion and celery; cook, stirring frequently, until softened and beginning to brown, 3 to 6 minutes. Sprinkle flour, dry mustard, salt and pepper over the vegetables and cook, stirring, for 1 minute more. Add broth and milk; bring to a gentle boil, stirring constantly.
Stir in broccoli and potatoes and bring just to a simmer. Simmer, uncovered, stirring occasionally, until the potatoes are tender, 12 to 15 minutes.
Add chicken and 1 cup Cheddar and cook, stirring frequently, until cooked through, 4 to 6 minutes. Serve topped with a little more Cheddar and red onion, if desired.