Mix the Sauce: Add the low-sodium soy sauce, beef broth, oyster sauce, hoisin sauce, mushroom soy sauce, toasted sesame oil, and cornstarch to a measuring cup.Whisk until the mixture is well combined, then set it aside. Brown the Beef: Heat a large nonstick pan over medium-high heat and spray it with oil. Add the ground beef and use a wooden spoon to break it into small pieces. Cook, stirring occasionally, until the beef is browned and cooked through. Add Aromatics: Add the finely chopped garlic and grated ginger to the cooked beef. Continue cooking for about 30 seconds, stirring as needed, until the aromatics become fragrant. Transfer the Beef: Move the cooked beef to a plate and set it aside while preparing the vegetables.
Clean the Pan: Use a paper towel to carefully wipe the skillet clean, then return the pan to the stove.
Cook the Cabbage: Add 1 teaspoon sesame oil to the hot skillet over medium heat. Add the sliced Napa cabbage and cook, stirring occasionally, for about 2 to 3 minutes, until the cabbage is just tender. Combine the Vegetables and Beef: Add the shredded carrot and reserved cooked beef to the skillet with the cabbage.Stir everything together until the ingredients are evenly incorporated. Add the Sauce: Pour the prepared sauce into the skillet and stir thoroughly so it coats the beef and vegetables.
Finish the Stir-Fry: Cook for 30 to 40 seconds, stirring, until the sauce thickens slightly and coats the meat well. Remove the skillet from the heat.
Serve: Spoon the finished beef and cabbage stir-fry over rice, if desired. Garnish with scallion greens and toasted sesame seeds before serving.