Marinate the beef with 1 tbsp soy sauce and a pinch of salt and pepper for 15 minutes.
Heat the oil in a pot over medium heat. Add the garlic and ginger, and sauté for 30 seconds.
Add the beef and cook until browned on all sides.
Add the tomato, beef broth, water, green onions, soy sauce, rice vinegar, and sugar. Bring to a boil, then reduce heat and simmer for 15 minutes, or until the beef is tender.
Push the soup to the side of the pot and pour in the beaten eggs. Let them cook undisturbed for a minute, then gently scramble them.
Season with salt and pepper to taste.
Serve the soup over cooked noodles.