1. Add the sliced onions and oil to a soup pot. Saute onions on medium heat until golden and clear. Do not make the heat too high or the onions will burn.
2. Add the celery, salt and pepper and continue to cook on medium heat.
3. Add the tomatoes and basil and cook for 15 minutes.
4. Add the water or broth, and bring to a boil.
5. Reduce heat and simmer for 20 - 30 minutes on medium - low heat. Taste and add additional salt and pepper to taste if needed.
6. Place a slice of the toasted bread in each of 6 small bowls.
7. Bring soup back to a boil.
8. Sprinkle the bread with the grated pecorino cheese, and break an egg over each slice of bread.
9. Add the boiling soup and serve as soon as the egg white is cooked.