Melt butter in a large saucepan over medium heat. Add onion; cook 2 1/2 minutes or until soft. Stir in potato and next 5 ingredients (through corn); bring to a boil. Reduce heat; simmer 15 minutes or until potato is soft. Remove 2 cups, purée, and return to pan.
Stir in sausage and milk over low heat; cook until thick (about 5 minutes). Remove from heat. Garnish with cheese and parsley.