Paper-thin slices of Vidalia and red onions figure prominently in this contemporary take on a traditional steak house salad.
Put onions into a large bowl of cold water. Swish onions with your hands until water becomes cloudy. Transfer onions to a clean bowl of cold water, and let soak 15 minutes. Repeat twice. Drain, and pat dry. Transfer to a large bowl.
Whisk together vinegar, honey, lemon juice, mustard, salt, and pepper in a bowl. Add oil in a slow, steady stream, whisking until emulsified.
Add radicchio, lettuce, tomatoes, and parsley to bowl with onions. Drizzle with dressing to taste, and toss. Serve with remaining dressing on the side.
The two onions are mild enough to eat raw, but they become even more tame after soaking them in ice water, a process that helps remove bitter compounds.