Warm the olive oil in a large skillet over medium-high heat. Add the ground beef and stir frequently, cooking until browned and no longer pink about 5 minutes. Season with sea salt and black pepper to your liking.
Mix in the diced onion and grated carrot with the beef, cooking for an additional 5 to 7 minutes while stirring every now and then, until the onion becomes tender.
Fold in the minced garlic and keep stirring for 30 seconds to release its aroma.
Add the thinly sliced cabbage, ground ginger, soy sauce, sesame oil, and granulated sugar to the pan. Cook everything together for 5 to 7 minutes, stirring occasionally, until the cabbage softens but still has a slight crunch.
Remove the skillet from heat and sprinkle the dish with chopped green onion and sesame seeds if you want a little extra flavor and texture. Serve immediately while warm.