Place eggs in a saucepan and cover with salted cold water. Bring to a boil, remove from heat, cover saucepan, and let eggs stand in hot water, 10 to 12 minutes. Drain water from saucepan and cover eggs with ice water until chilled, about 10 minutes. Peel eggs and chop or shred.

Fill a large pot halfway with water; bring to a boil. Add potatoes, rice, green onions; reduce heat and simmer until potatoes are mostly tender, 15 to 20 minutes. Add spinach and parsley; continue simmering until wilted, 5 to 7 minutes.

Stir sour cream into soup until well mixed; add dill. Bring soup back to a boil, remove pot from heat, and stir eggs into soup. Season with salt.