Mix the soy sauce, hoisin sauce, sesame oil, minced garlic, grated ginger, and red pepper flakes in a small bowl to make the sauce.
Heat one tablespoon of vegetable oil in a large skillet over medium-high heat. Add the sliced beef and cook for two to three minutes until it browns on the edges. Remove the beef to a plate.
Add the remaining tablespoon of vegetable oil to the same skillet. Toss in the broccoli florets and stir-fry for three minutes until they turn bright green and start to soften.
Return the beef to the skillet. Pour the prepared sauce over everything and stir well so the beef and broccoli are coated. Cook for another two minutes until the sauce thickens slightly.
Spoon the cooked brown rice into four bowls. Top each bowl with the beef and broccoli mixture.
Finish with sliced green onions and a sprinkle of sesame seeds before serving.