Fill a large pot with water and bring it to a boil. Carefully add the beet, potatoes, and carrots. Lower the heat to medium-low and simmer the vegetables until they are fork-tender. (Refer to Note 1 for suggested cooking times for each vegetable.)
Meanwhile, warm the olive or sunflower oil in a large sauté pan over medium heat. Add the minced onion and sauté for about 5–7 minutes, stirring occasionally, until softened and translucent. Using a slotted spoon, transfer the sautéed onions to a small bowl and set aside.
When the vegetables are cooked, gently remove them from the pot and submerge them in a bowl of cold water to cool quickly. Once cooled enough to handle, peel the skins off the beet, potatoes, and carrots. Dice them into small, uniform cubes, along with the dill pickles.
In a large mixing bowl, combine the diced vegetables, green onion, sweet peas, sautéed onion, salt, and pepper. Mix everything together gently until well combined.
Serve and savor this vibrant and flavorful Vinegret Salad as a side dish or a light meal!