Halve beets and place in a vegetable steamer set over boiling water. Steam, covered, until tender when pierced with the tip of a knife, 20 to 35 minutes depending on size. Let cool. Use a paring knife to pull off loosened skins. Cut beets into ½ inch cubes.
Meanwhile, place potatoes in a saucepan and cover with water. Bring to a boil and cook covered, until almost tender, about 15 minutes. Add carrots and cook until potatoes are tender and carrots are crisp-tender, about 5 minutes more. Drain and let cool. With a paring knife, peel loosened skins from potatoes and cut potatoes into ½ inch cubes.
In a large salad bowl, combine beets, potatoes, carrots, pickles, onion and half the dill. In a small bowl, whisk together oil, vinegar, mustard, salt and pepper until blended. Pour over vegetables and gently fold to combine. Serve at room temperature or chilled. Just before serving, spoon peas over the top of the salad and sprinkle with remaining half of the dill.