Heat olive oil in a large skillet over medium-high heat. Add the ground beef and cook until no longer pink, about 5 minutes, breaking it up with a spatula as it cooks. Season with salt and pepper.
Add the onion and carrot, and sauté until the onion is tender (about 5-7 minutes), stirring occasionally. Add the minced garlic and cook for another 30 seconds, stirring constantly.
Finally, add the cabbage, ground ginger, soy sauce, sesame oil, and granulated sugar. Continue sautéing for 5-7 minutes, stirring occasionally, until the cabbage is tender.
Serve garnished with chopped green onion and sesame seeds, if desired.