Prep the Vegetables: Begin by chopping the cauliflower into small florets, shredding the carrot, and chopping the celery.
Cook the Vegetables: In a large saucepan, combine the cauliflower, carrot, celery, water, and bouillon. Bring to a boil, reduce heat, cover, and simmer for 12-15 minutes until vegetables are tender.
Make the Roux: In another large saucepan, melt the butter over medium heat. Stir in the flour, salt, and pepper until smooth. Gradually add the milk, stirring constantly until the mixture is thick and bubbly.
Combine and Cook: Slowly add the vegetable mixture to the roux, stirring well. Bring the soup to a gentle boil and cook for 2 minutes until thickened.
Add Cheese: Reduce heat and stir in the shredded cheddar cheese until melted. Add hot pepper sauce if desired.
Serve: Ladle the soup into bowls and enjoy hot.
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