Directions
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Melt butter in a stock pot over medium-high heat; add onion and saute until tender, 3 to 4 minutes. Whisk in flour and continue to stir until mixture turns golden brown, about 5 minutes. Slowly add half-and-half to onion mixture, stirring until mixture is smooth. Add chicken broth; season with salt and ground black pepper.
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Reduce heat to medium-low and simmer mixture until thickened, about 10 minutes. Add broccoli, carrot, and celery. Simmer until vegetables are tender yet crisp, about 20 minutes.
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Reduce heat to low. Add Cheddar cheese to soup and cook, stirring occasionally, until cheese melts, about 5 minutes.
