Mix beets, eggs, breadcrumbs, walnuts, salt, and pepper in a bowl.
Heat pan over medium-high heat, add 1/2 the oil, form three cakes with half the beet mixture and add to the pan. Cook ~4-5 minutes on each side and place on paper towel to drain excess oil. Repeat with remaining beet mixture.
Sprinkle with parsley and serve with sour cream or yogurt.