When hot, add the onions. Saute until translucent and add the Italian sausage. Break apart the sausage with a spoon and stir occasionally. When the sausage is brown remove from heat.
In a soup pan, combine the potatoes, chicken stock, and celery. Over medium-high heat, bring to a boil.
Reduce heat to medium and simmer for 20 minutes, or until the potatoes are tender.
Use a slotted spoon to transfer the cooked sausage and onions to the soup pot. Add the cream and cheddar cheese, stirring until all ingredients are combined and warm again. Serve with additional cheddar cheese and green onions sprinkled on top.