Trim any fat and sinew from the fillet. Tie thyme and rosemary bunches together. Dip herb brush in oil, brush fillet lightly with oil. Season with salt and pepper.
Heat the barbecue to a high heat, place beef fillet on the barbecue and sear for 15 minutes, turning every 3-4 minutes. Move fillet to indirect heat, cover with the barbeque lid and cook, turning once.
Cook beef until core temperature is 56°C for medium rare consistency or until cooked to your liking. Remove beef to a carving board, cover loosely with foil, leave to rest for 10 minutes.
Slice beef into 1cm thick slices, serve with roast vegetables, char grilled aspargus and jus.
