1. Gather all the ingredients: lean ground beef, chopped cabbage, diced onion, minced garlic, julienned or grated carrots, olive oil or vegetable oil, soy sauce or coconut aminos, tomato paste, paprika, salt, pepper, and optional ginger and red pepper flakes.
2. Heat a large skillet or wok over medium-high heat.
3. Add 1 tablespoon of oil to the skillet and allow it to heat up.
4. Place the ground beef in the skillet and cook, breaking it into small pieces using a wooden spoon.
5. Allow the beef to cook for 5-7 minutes, or until it is browned and no longer pink.
6. Use a slotted spoon to remove the cooked beef from the skillet and set it aside on a plate.
7. If needed, add the remaining tablespoon of oil to the skillet.
8. Add the diced onion to the skillet and sauté for 2-3 minutes until softened.
9. Stir in the minced garlic (and grated ginger if using) with the onions, cooking for 30 seconds to a minute until fragrant.
10. Add the chopped cabbage and julienned carrots to the skillet, stirring to combine them with the onion and garlic mixture.
11. Cook the vegetables for 5-7 minutes, stirring occasionally, until the cabbage begins to wilt and the carrots soften slightly.
12. Stir in the tomato paste, soy sauce, paprika, salt, and pepper to season the vegetable mixture.
13. Return the cooked ground beef to the skillet, mixing it thoroughly with the vegetables and seasonings.
14. Allow the entire mixture to cook for 3-5 more minutes, giving the flavors time to blend.
15. If the stir fry seems too dry, add a splash of beef broth or water to create a slight sauce consistency.
16. Taste the stir fry and adjust the seasonings to your liking, adding more soy sauce, salt, pepper, or red pepper flakes if desired.
17. Serve hot and enjoy your quick and easy cabbage and ground beef stir fry with an accompaniment like rice, noodles, or on its own.