Combine rice, salt, and 2 ¼ cups water in a medium-sized pot with tight-fitting lid. Bring to a boil, then reduce heat and simmer, covered, until all water is absorbed, 15 minutes. Turn off heat and let sit 10 minutes, then remove lid and fluff with a fork.
Meanwhile, in a medium bowl, whisk together soy sauce, chicken broth, vinegar, brown sugar, garlic, sesame oil, cornstarch, ginger, and Sriracha.
In a large deep-sided skillet, heat olive oil. Cook steak in batches until nicely browned, about 4 minutes, then transfer to a plate.
Add remaining olive oil to skillet along with broccoli and red pepper and cook until broccoli is bright green, 1 to 2 minutes. Add ½ cup water and let steam, covered, until vegetables are tender-crisp, 2 to 3 minutes.
Add sauce and steak to skillet and bring to a boil. Let simmer until thickened, 3 minutes more.
Serve beef and broccoli with cooked rice and garnish with crushed red pepper, if using.