In a small bowl, whisk together soy sauce, brown sugar, sesame oil, minced garlic, grated ginger, and crushed red pepper flakes until sugar is dissolved. Set aside.
Heat olive oil in a large skillet over medium-high heat.
Add the lean ground beef to the skillet and cook, breaking it apart with a spatula, until browned and cooked through, about 6 to 8 minutes.
Drain excess fat from the skillet if necessary.
Add the chopped broccoli and julienned carrot to the skillet with the beef and cook for 3 to 4 minutes until vegetables are tender-crisp.
Pour the soy sauce mixture over the beef and vegetables and stir well to combine.
Cook for an additional 2 minutes, allowing the sauce to thicken slightly and coat the beef and vegetables evenly.
Remove from heat and stir in chopped green onions and toasted sesame seeds.
Serve immediately with steamed rice or your preferred side.