Finely chop the cilantro, dill, and optional green onion, then transfer to a mixing bowl. Add the ground beef to the bowl.
Grate the onion and add it to the mixing bowl. Mix the ingredients thoroughly.
Add the egg, salt, black pepper, and red pepper to the mixture. Mix everything together by hand until well combined.
Rinse about 1.5 ounces of uncooked rice, then add it to the meat mixture. Mix again by hand until evenly distributed. Set aside the remaining rice for the soup.
Using a tablespoon measure for consistent sizing, scoop the meat mixture and roll it into small, even-sized meatballs by hand. Set them aside.
Fill a pot with water and bring it to a boil. Add salt, then carefully drop the raw meatballs into the water. Cook until the meatballs are fully cooked through. Strain the meatballs and remove any bits that may have broken off during cooking.
In a clean pot, fill with water and bring it to a boil. Add salt, then return the cooked meatballs and any remaining pieces to the pot.
Peel and chop the potatoes, then add them to the pot.
Stir in the tomato paste, pepper paste, and butter. Add the remaining rice to the pot.
Cook the soup over low heat until the potatoes and rice are tender. Adjust seasoning if needed.
Serve the soup hot and enjoy its hearty flavors!