Heat a large skillet over medium-high heat. Add the ground beef and cook for 7-10 minutes, breaking it apart as it browns. Once fully cooked, transfer it to a plate and set aside.
While the beef cooks, whisk together the coconut aminos, garlic, ground ginger, rice vinegar, chili garlic sauce, and sesame oil in a small bowl. Set the sauce aside.
Add the bell pepper, onion, cabbage, broccoli, mushrooms, and shredded carrot to the same skillet. Sauté for about 10 minutes, stirring every few minutes, until the vegetables are tender but still have a slight crunch. Covering the skillet with a lid will help them cook more quickly.
Meanwhile, cook the ramen noodles according to the package directions. Drain and set aside.
Return the cooked ground beef to the skillet, then add the cooked noodles and prepared sauce. Toss everything together until evenly coated and heated through.
Garnish with sliced green onions and sesame seeds before serving.