Trim the excess fat off the fillet with a sharp knife. Fold the thin end of the tip underneath the fillet so the fillet is around the same thickness throughout. Tie the folded end of the beef tenderloin together with butcher's twine, then tie the roast to the twine every 1/2 to 1 inches (to help the roast keep its shape while cooking). Snip the silverskin with scissors to keep the roast from bowing while cooking.
Pat dry your beef with a paper towel, then cover well with oil. Spread freshly cracked black pepper and sea salt on a plate of enough size to fit the fillet. Roll the fillet in the mixture so that it is well covered. You might need more salt and pepper depending on your taste buds.
Once the fillet is well seasoned, place your rosemary sprigs and whole garlic cloves on the plate and place your fillet on top. Cover and chill for up to 24 hours. Ensure that the temperature of your fillet is around 1 hour before cooking.
Either build a charcoal fire in half the grill or turn the burners over the barbecue grill according to your units manufacturers instructions. Use tongs to lubricate the grate with an oil-soaked rag or paper. Put beef on the hot side of your grill and close the lid. Grill until seared on each side, about 3 minutes per side.
Move meat to the cool side of the grill (if you only have 1 or two burners just sit the fillet to one side and keep one burner on medium).
In a medium sauce pan, melt half a stick of butter, 1 finely chopped rosemary sprig, 2 finely chopped gallic cloves and salt and pepper to taste. For the last 30 minutes of cooking time, baste the fillet 3 times with a mixture of melted butter.
Cook until your meat thermometer reads 125 degrees F in the centre of the thickest part for rare. Usually about 45 to 60 minutes, depending on the size of the filet and the grill.
Take off the grill and cover with foil and let the meat rest 15 minutes before slicing.