Whisk together soy sauce, brown sugar, sesame oil, cornstarch, garlic, ginger, crushed red pepper, and sriracha in a small bowl. Set aside.
Season beef strips with salt and pepper.
Heat 2 tablespoons of sesame oil in a large skillet or sauté pan over medium high heat. Add beef strips and cook for 5 to 6 minutes, or until done and no longer pink.
Remove steak from skillet using tongs or a slotted spoon (leaving juices in skillet) and place on a plate. Set aside.
Add broccoli to the same skillet and sauté until tender (stirring frequently), about 4 to 5 minutes.
Return the beef to the skillet with the broccoli. Whisk the sauce mixture again a few times and pour it into the skillet. Stir to coat as evenly as possible.
Cook, stirring often, until the sauce has thickened (about 2 to 3 minutes).
Serve with cooked white rice and sprinkle with sesame seeds when serving (if desired).