Bring the chicken stock, water, onion, garlic, bay leaves and saffron to a boil. Add the orzo. Cook until the orzo is soft and tender, about 8-9 minutes. Remove the onion and bay leaves. Turn the heat off and remove 1 cup of hot stock.
Meanwhile, in a medium-sized bowl, whisk the eggs. Add the 1 cup of hot stock to the eggs, a quarter cup at a time. Be sure to quickly stir the eggs while pouring in the hot liquid to prevent the eggs from scrambling. Continue this process until the eggs are warmed through.
Add the butter, lemon zest and lemon juice into the orzo soup. Stir until melted. Slowly add the tempered eggs to the soup, stirring the soup constantly while the egg mixture is being incorporated into the soup.
Add the cheese and stir well. Serve warm topped with freshly chopped parsley leaves.