How to Make It
Preheat the oven to 450°. Wrap the beets in foil and roast for about 1 hour, until tender. Let cool slightly, then peel.
Meanwhile, in a saucepan, cover the potatoes and carrots with at least 2 inches of water and boil until tender, about 15 minutes for the carrots and 20 minutes for the potatoes. Let cool to room temperature. Grate the potatoes on the medium holes of a box grater and transfer to a small bowl. Repeat with the carrots and beets, keeping the vegetables in separate bowls.
Halve the eggs. Push the egg whites through a fine sieve into a small bowl. Clean the sieve, then push the yolks through into another small bowl.
In another bowl, mix the herring with the onion, oil and chopped dill.
In a small bowl, mix the mayonnaise with 2 tablespoons of the grated beets.
Place a 4-inch round ring mold in the center of a serving plate. Using the back of a spoon, spread one-fourth of the grated potatoes inside the mold in an even layer. Season with salt. Spread one-fourth of the herring mixture on top in an even layer. Repeat the layering with one-fourth each of the carrots and beets. Season with salt. Spread 2 tablespoons of the beet mayonnaise on top. Garnish with some of the sieved egg whites, sieved egg yolks and dill sprigs. Carefully remove the ring mold and wipe it clean. Repeat to form 3 more molded salads.