1. Preheat the oven to 425°. Wrap the beets in foil and bake for about 1 hour, or until tender when pierced. When cool enough to handle, peel the beets and cut them into 2-by- 1/2 -inch matchsticks or small wedges.
2. Bring a medium saucepan of lightly salted water to a boil. Add the haricots verts and cook until tender, about 4 minutes. Using a slotted spoon, transfer the beans to a colander and rinse under cool running water; pat dry. Pour off all but 2 inches of water from the pan and set a steamer basket inside. Add the potatoes and steam until tender, about 18 minutes. Let cool slightly, then quarter the potatoes.
3. In a medium bowl, combine the shallots, horseradish, vinegar, sour cream and mustard. Whisk in the oil, 1 tablespoon at a time, until emulsified. Whisk in the heavy cream and season with salt and pepper.
4. Just before serving, stir the dill into the dressing. In a bowl, toss the flaked trout with 1/4 cup of the dressing and mound on 4 large dinner plates. Garnish each serving with the beets, haricots verts, potatoes, eggs and tomatoes. Pass the remaining dressing separately.
Make Ahead: The vegetables and dressing can be refrigerated overnight.