Into a large soup pot, combine the cauliflower, carrot, celery, and chicken-style broth. Bring just to a boil then reduce heat to low. Cover and simmer for 10 minutes, until vegetables are fork-tender. Remove from heat and set aside; do not drain.

Into a large saucepan over medium heat, add the butter. When the butter is melted, whisk in the flour, salt, and pepper. Gradually add milk, whisking continuously until fully incorporated. Bring to a low boil and continue cooking for 2 minutes, until thickened.

Reduce the heat to low and add the cheddar cheese. Stir continuously for 1 minute, until the cheese is melted.

Pour the cheese sauce into the pot with the cooked vegetables, stirring to fully combine. Adjust seasoning to taste and serve hot.