Place the lamb steak into a bowl with the rosemary, garlic and oil and stir. Leave to marinate for ten minutes, or longer if possible.
Heat a griddle pan until very hot. Remove the lamb steak from the marinade and season with salt and freshly ground black pepper. Griddle for two minutes on each side for medium-rare meat, or longer if you like it well done. Remove the lamb from the pan and leave to rest.
Place the broccoli onto the griddle and cook, turning frequently, until chargrilled.
To serve, place the broccoli onto a serving plate and top with the lamb steak. Drizzle over the melted butter and sprinkle with parsley.