Put beans into a 4-qt. saucepan and cover with 2″ water. Bring to a boil and cook for 1 minute. Skim any foam from surface and drain beans; set aside.
Heat oven to 325°. Heat oil in a 6-qt. Dutch oven over medium-high heat. Season beef with salt and pepper; add to pot and cook, turning, until well browned, about 8 minutes. Transfer beef to a plate. Add garlic, onions, and paprika to pot and cook, stirring, until onions are soft, about 10 minutes. Add the reserved beans, the beef, tomatoes, barley, potatoes, eggs (in the shell), parsnips, carrots, and 8 cups water to cover; season with salt and pepper and bring liquid to a simmer. Cover pot and transfer to oven. Bake until beef is tender, about 2½ hours. To serve, transfer beef to a cutting board and cut into pieces (if not already pre-cut). Remove eggs; peel and chop. Divide beef and eggs between 6 serving bowls and spoon stew into bowls. Garnish with parsley.