Scrub the beets and the large radishes but do not peel. Trim the leafy stem end off and slice on the 1/8 inch setting of your mandolin. This may take a bit of trial and error to get the slices just right. You want them to be thin and almost translucent. Put the slices on a wet plate and cover with a wet kitchen towel while you work.
Peel the carrots and slice them the same way. Be very careful of your fingers when you are doing this. Use the safety guard provided with your mandolin whenever possible.
To assemble your salads, put a layer of dill or a leaf or two of lettuce on each of 4 small plates.
Start with the largest rounds and layer the vegetables in a loose stack. Top with the smaller carrots.
Drizzle with olive oil and balsamic glaze. Lightly sprinkle with salt and pepper and serve right away.