Season the steaks with salt and pepper. Heat a large pan over high heat. Add the avocado oil and when hot, add the steaks. Cook, turning occasionally, until browned, about 8-10 minutes for medium-rare, or until cooked to your desired doneness. A minute before removing the steaks, add the coconut aminos and rice vinegar, turning steaks in resulting sauce. Set steaks and any resulting sauce aside and cover with foil, allowing it to rest while you prepare the vegetables. Wipe the pan clean.
While steaks cook, mix softened butter with miso until completely smooth, set aside.
Add more avocado oil to the pan so that the bottom is completely covered with a thin coating, about 5 tablespoons will be needed for a 12-inch pan. When hot, add the broccoli. Season with a bit of salt and add a couple of tablespoons of water. Cook, covered over high heat without stirring or turning for about 4 minutes. Remove cover and cook without moving for another 4-5 minutes, or until broccoli is golden brown where it is in contact with the pan. Finally, flip broccoli and cook until second side is browned, another 4 minutes or so. Off heat, drizzle with toasted sesame oil.
While broccoli is cooking, combine the mayonnaise and aioli with a tablespoon of coconut aminos. Set aside.
To serve, slice steak across the grain (for a more tender bite), top with half the miso butter, sprinkle with togarashi seasoning. Serve broccoli along side with aioli.