Leftover dressing can be stored in refrigerator up to seven days.
Whisk together mayonnaise and next 6 ingredients in a medium bowl. Let stand 30 minutes.
Arrange lettuce on a serving platter or individual plates. Top with cucumber and onion; sprinkle with Parmesan cheese. Serve with dressing.
*1 (4-oz.) envelope buttermilk Ranch dressing mix may be substituted.
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