Toss the sliced beef in cornstarch and set it aside.
In a small mixing bowl, whisk together the soy sauce, brown sugar, garlic, ginger, salt, pepper, and red pepper or chili paste (if desired). Set aside.
Place a large skillet over medium heat, and add a tablespoon of olive oil. Once the oil is hot, add the beef and cook until browned on all sides, remove from the pan and transfer to a plate.
Add the remaining oil to the pan. Add the onion and sauté for 1 minute. Then, add the broccoli florets and cook for 3 minutes. Return the beef to the pan, add the sauce, and cook for 2-3 minutes or until the beef is coated in a thick, sticky sauce and the broccoli is fully coated.
Serve immediately.
Notes
To STORE Beef and Broccoli, place in an airtight container in the refrigerator for up to 3-4 days. While it's possible to freeze it, the texture of the broccoli may change upon thawing.For REHEATING, gently warm it in a skillet over medium heat until heated through, or use the microwave, stirring occasionally to ensure even heating. If frozen, thaw in the refrigerator overnight before reheating.