Heat the Oil: In a large pot or Dutch oven, heat 1 teaspoon of oil over medium heat until it shimmers.
Sauté Onions and Garlic: Add the diced onion to the pot and cook for about 3 minutes until it becomes translucent. Add the minced garlic and cook for another minute, until fragrant.
Add Carrots: Stir in the sliced carrots and cook for about 5 minutes, until they start to soften.
Cook the Beef: Push the vegetables to one side of the pot and add the lean ground beef. Cook, breaking it up with a spoon, until it is browned and cooked through, about 5-7 minutes.
Add Cabbage and Seasonings: Stir in the shredded cabbage and cook until it begins to wilt, about 3-4 minutes. Add the grated ginger, soy sauce, and oyster sauce. Stir well to combine.
Add Broth and Simmer: Pour in the beef broth, add the salt and black pepper, and stir to combine. Bring the soup to a boil, then reduce the heat to low and let it simmer for about 15-20 minutes. This allows the flavors to meld together.
Add Green Onions: Stir in the chopped green onions and let the soup cook for an additional 2-3 minutes.
Serve: Ladle the hot soup into bowls and serve immediately. Enjoy the comforting, savory flavors of this egg roll-inspired soup.