In a small bowl, whisk together the soy sauce, water, brown sugar, rice vinegar, sesame oil, cornstarch, and crushed red pepper flakes until smooth. Set aside.
Heat a large skillet or wok over medium-high heat. Add the ground beef and season with the salt and black pepper.
Cook the beef for 5–6 minutes, breaking it into bite-sized crumbles, until browned and cooked through.
Drain any excess grease from the skillet. Transfer the cooked beef to a plate and set aside.
Add the avocado oil to the same skillet. Add the bell pepper, broccoli, and carrots.
Cook the vegetables for 4–5 minutes, stirring frequently, until crisp-tender.
Add the garlic and ginger. Cook for 30 seconds, stirring constantly, until fragrant.
Return the cooked ground beef to the skillet.
Whisk the prepared sauce once more, then pour it over the beef and vegetables.
Cook for 2–3 minutes, stirring frequently, until the sauce thickens and coats the stir-fry evenly.
Remove from the heat. Garnish with the green onion and sesame seeds. Serve immediately over cooked rice.