Place beets into a large pot and cover with water. Bring to a boil over high heat, then reduce the heat to medium-low, cover, and simmer for about 20 minutes. Add carrots and potatoes; boil for 10 more minutes. Remove from the heat and leave the pot covered, 8 hours to overnight.

Peel and dice beets, carrots, and potatoes into small, even pieces. Place vegetables into a large bowl. Stir in onion, peas, pickles, olive oil, salt, and pepper. Garnish with parsley before serving.