In a large pot, heat up the olive oil and 2 tablespoons of the butter, over medium heat. Season with salt and pepper.
Add the cauliflower florets and stir with a wooden spoon. Cook for 5 minutes.
Add celery, onion and thyme and cook for 3 more minutes.
Push the vegetables to 1 side of the pot. Melt 1 more tablespoon of butter on empty side of pot and add flour to the butter.
Cook the rue (flour/butter) for 1 minute, stirring the flour in the butter.
Mix in chicken broth and half-and-half. Bring up to a simmer and cook for 15 minutes.
Puree soup using an emersion blender, food processor or blender and return to pot. I like to leave it a little chunky. Check seasoning and add a dash of hot sauce, if desired.
Serve hot with a side of garlic bread.