Cook the Vegetables: In a large pot, combine cauliflower, shredded carrot, celery, water, and chicken bouillon. Bring to a boil, then reduce heat and simmer for 10–12 minutes until vegetables are tender.
Prepare the Roux: In a separate saucepan, melt butter over medium heat. Stir in flour, salt, and black pepper, whisking constantly for 1–2 minutes until smooth.
Add the Milk: Slowly whisk in the milk, stirring continuously until thickened.
Combine Everything: Pour the milk mixture into the pot with the cooked vegetables. Stir well and bring to a gentle simmer.
Melt the Cheese: Remove from heat and stir in the shredded cheddar cheese until fully melted and creamy.
Serve & Enjoy: Ladle into bowls and serve warm. Garnish with extra cheese or fresh herbs if desired.