In a small saucepan of 2 cups water, cook rice according to package instructions; set aside.
Preheat oven to 450 degrees F. Lightly oil a baking sheet or coat with nonstick spray.
In a large bowl, combine steak, 1 tablespoon soy sauce and 2 teaspoons brown sugar. Place steak and broccoli in a single layer onto the prepared baking sheet.
Place into oven and bake until steak is browned and broccoli is just tender, about 16-18 minutes.
In small saucepan over medium low heat, combine sesame oil, garlic, ginger, red pepper flakes, remaining 2 tablespoons soy sauce and remaining 2 tablespoons brown sugar. Bring to a boil; reduce heat and simmer, stirring constantly, until slightly thickened, about 2-3 minutes.
Serve steak and broccoli immediately with rice, drizzled with soy sauce mixture and garnished with green onions and sesame seeds, if desired.