Combine onion and margarine or butter in a 1½-quart microwave-safe bowl, covered, on 100 percent power (high) for 1½ to 2½ minutes or till onion is tender, stirring once.
Stir in cornstarch and pepper.
Add milk and Worcestershire sauce.
Cook, uncovered, for 2 to 4½ minutes or till slightly thickened and bubbly, stirring every minute (mixture will appear curdled).
Stir in American cheese, cream cheese, and parsley.
Cook, uncovered, on high for 3 to 4 minutes or till cheese is melted and mixture is heated through, stirring every minute.
Keep dip warm in a fondue pot over fondue burner, or reheat in casserole, as necessary, on 50 percent power (medium) for 2 to 3 minutes.
Serve with vegetable dippers and/or chips.