In a large pot, heat the vegetable oil over medium heat. Add the chopped onion and sauté until translucent, about 3-4 minutes. Stir in the minced garlic and grated ginger, cooking for an additional minute until fragrant.

Pour in the beef broth, soy sauce, sesame oil, and black pepper. Bring the mixture to a boil, then reduce the heat to a simmer.

Add the julienned carrots and chopped bok choy to the pot. Let the vegetables cook for about 5 minutes until tender.

Carefully add the frozen dumplings to the soup and cook according to package instructions, usually about 5-7 minutes.

While the dumplings are cooking, slowly drizzle the beaten eggs into the soup, stirring gently to create egg ribbons.

Once the dumplings are cooked, remove the pot from heat. Taste and adjust seasoning if necessary.

Serve the soup hot, garnished with sliced green onions and a sprinkle of sesame seeds.