Prepare the artichokes; cut off the stem and cut off two-thirds of the tops, leaving at least one-inch bottoms. Cook the bottoms; then cool them slightly, and with a spoon scoop out and discard the fuzzy "chokes". Return the artichokes to the cooking liquid and keep them warm.

Prepare coals of grill: place coals on each side so that the meat is not directly over medium hot coals. Rub pepper over the beef loins, then sprinkle with salt. Grill until a meat thermometer registers 145 F. (medium rare).

To serve, with a slotted spoon, remove the artichoke bottoms from the cooking liquid, and drain them on paper towels. Spoon some bearnaise sauce into the center of the artichokes. Slice the meat thickly; arrange the meat on the center of a warm platter and surround with the stuffed artichokes.