Melt butter in a large saucepan over medium heat; add squash and onion. Cover and cook 13 minutes or until squash and onion are very tender.
Transfer squash mixture to a food processor bowl; puree until smooth. Return squash mixture to saucepan. Stir in broth and next 4 ingredients; cook, uncovered, over low heat until thoroughly heated.
To serve, ladle 1 cup soup into each of 4 individual serving bowls, and top evenly with Parmesan cheese.