1. Cook first 3 ingredients in boiling water to cover in a Dutch oven 10 to 12 minutes or just until tender; drain well in a colander, gently pressing squash mixture against sides with a wooden spoon.
2. Stir together squash mixture, Cheddar cheese, and next 5 ingredients. Spoon into a lightly greased 6-qt. oval-shaped slow cooker. Sprinkle Parmesan cheese over top.
3. Cover and cook on LOW 2 1/2 to 3 hours or until center is set and edges are golden brown; uncover and cook 30 minutes. Let stand 10 minutes.
Note: Yellow squash, zucchini, and onions may be cooked and drained as directed up to 2 days ahead. Cover and chill until ready to assemble casserole.