Cut the vegetables and beef into thin slices.
In a small bowl, whisk together the soy sauce, beef broth, brown sugar, cornstarch, garlic, and ginger. Set the sauce aside for later use.
Preheat a large ceramic non-stick skillet over medium heat and add 1 tablespoon of oil.
Add half of the beef and cook uncovered for 3-4 minutes on each side until browned. Transfer the cooked beef to a bowl and repeat with the remaining beef.
Return the skillet to high heat and add the sliced mushrooms. Cook for about 3 minutes or until they turn brown. Transfer the mushrooms to a plate and set aside.
Add the remaining tablespoon of oil to the skillet and toss in the sliced bell peppers and onions. Cook for 2-3 minutes, stirring once or twice, until the veggies have softened slightly. Transfer the cooked vegetables to a plate and set aside.
Lower the heat to medium and add the chopped broccoli to the skillet. Whisk the stir fry sauce again and pour it into the skillet. Stir until it comes to a boil and cook for a few minutes until thickened, stirring often.
Add the cooked beef, mushrooms, onions, and bell peppers back into the skillet. Stir gently to combine, then turn off the heat.
Garnish with sesame seeds and serve immediately over rice, quinoa, or whole wheat spaghetti.