Heat 2 tablespoons oil in a large flat-bottom wok or cast-iron skillet over medium-high heat. Add the steak and cook, stirring once, until browned, about 4 minutes. Transfer to a clean plate. Add the remaining 1 tablespoon oil and broccoli; cook, stirring occasionally, until slightly tender, about 2 minutes. Stir in scallions, ginger and garlic; cook, stirring, until fragrant, about 30 seconds. Whisk the tamari mixture and add it, along with the beef, back to the pan; cook until the sauce thickens, about 1 minute. Serve over brown rice and garnish with crushed red pepper, if desired.