In a soup pot over medium heat, melt the butter and sauté the onions and celery until tender, for about 5 minutes.
Add the garlic and thyme and stir for another minute. Sprinkle in the flour and mix until it is well absorbed. Pour in the broth, milk and cauliflower and bring the soup to a boil.
Once the soup is boiling reduce the heat and simmer the soup for 20 minutes, stirring occasionally until the cauliflower has softened.
Remove the soup pot from the heat. Using an immersion blender, purée the soup until it is well blended. Add the cheddar cheese and a splash of milk if you desire a thinner consistency.
Top each bowl with additional shredded cheddar cheese and crispy crumbled bacon bits.