Heat a small pot over medium heat. Add the olive oil, green onions, and ginger. Stir and cook for one minute. Add the garlic and cook an additional minute.

Add the tomatoes, stir and cook until the tomatoes are broken down and jammy, about 2 minutes. Add salt, to taste.

Add the broth, soy sauce, and rice vinegar. Add the dumplings and cook until the dumplings are cooked through (according to package instructions).

While the dumplings cook, crack the eggs into a small bowl and whisk until well combined.

Turn the heat to low. While stirring the soup, slowly pour in the egg. Turn off the heat. Add a splash of sesame oil. Transfer to a bowl and serve.