In a large pot, sauté the sausage, onion, and celery over medium heat until the onion is translucent. Season with salt and pepper. Add garlic and cook briefly before mixing in the flour to create a roux.
Gradually pour in the chicken broth, milk, and heavy cream, stirring continuously to blend the roux into the liquid. Season with Cajun spice and add the potatoes. Simmer until the potatoes are fork-tender.
Serve the soup hot, garnished with shredded cheddar cheese and sliced green onions. DEVOUR!