Steam brussels sprouts in batches until just tender, about 12 minutes. Transfer to colander; cool. Transfer to large bowl.
Mix vinegar and mayonnaise in small bowl. Gradually mix in oil. Season with salt and pepper. (Brussels sprouts and dressing can be made 1 day ahead. Cover; chill.)
Add apples and celery leaves to brussels sprouts. Add dressing; toss to combine. Mix in cheese and walnuts. Season with salt and pepper. Line large bowls with radicchio leaves. Add salad; serve.
In the mood for something other than Brussels Sprouts? Check out all of the recipes that I whipped up on Gardening with Ciscoe. I confess that I had a little help from PCC Cooks Chef Lynne Vea.