In a 4- to 6-quart Dutch oven, cook potatoes, covered, in enough lightly salted boiling water to cover for 20 to 25 minutes or until tender. Add garlic to the potatoes the last 15 minutes of cooking.
Meanwhile, in a food processor, combine Parmesan cheese, sour cream, and butter. Cover and process until just smooth.
Drain potatoes and garlic; transfer to a very large mixing bowl. Add cheese mixture, salt, and pepper. Beat with an electric mixer on low speed or by hand until potatoes are smooth. Stir in green onion. If you like, top with a pat of butter. If you like, add milk to reach desired consistency. Makes 12 (2/3-cup) servings