In a large pot or dutch oven, place the cauliflower florets, shredded carrot, chopped celery, and onion. Pour the chicken stock over the veggies. Bring to a boil, reduce heat and simmer for 15 mins until veggies are tender.
In a small saucepan, melt the butter and add the flour. Cook this mixture for a couple of minutes and whisk in the milk. Cook until thickened.
Remove the saucepan from the heat and blend in the shredded cheese until melted.
Pour the cheese mixture into the pot with the veggies.
Add the bay leaves, dried basil, salt, and pepper. Simmer for 10 mins. Adjust seasoning before serving and add more salt if needed.