Heat oven to 425°F. Combine Greek seasoning and black pepper; roll roast in rub mixture to cover all surfaces.
Place roast on rack in a shallow roasting pan. Insert ovenproof meat thermometer so tip is centered in thickest part of beef. Do not add water or cover. Roast in 425°F oven 35-45 minutes for medium rare; 45-50 minutes for medium doneness.
Remove roast when meat thermometer registers 135°F for medium rare; 145°F for medium. Transfer roast to carving board; tent loosely with aluminum foil. Let stand 15-20 minutes.(Temperature will continue to rise about 10°-15°F to reach 145°F for medium rare; 160°F for medium.)
Carve roast into slices. Season with salt, as desired.
Season Beef Tenderloin Roast generously with salt and pepper.
Lightly coat grates with vegetable oil spray. Close cooking chamber lids.
Place 3-5 lbs. of charcoal, in center of the firebox. Open the firebox air vent approximately 1-2″, and smokestack damper halfway. With firebox lid open, stand back, carefully light charcoal and allow to burn until covered with a light ash. (Approximately 20 minutes)
Once coals have ashed over, add wood chunks. Do not shut firebox lid until the smoke is clean, often called Blue Smoke.
Close firebox lid. Adjust the firebox air vent and smokestack damper to regulate cooking temperature. The ideal smoking temperature is 300°F.
Place Tenderloin on cooking grate in cooking chamber. Maintain a consistent cooking temperature by adding wood chunks as needed. Rotate Tenderloin a quarter turn every 20 minutes. About 45 minutes-1 hour. Monitor the internal temperature of the sparingly throughout the cooking process. The ideal finished internal temperature is 135°F.
Remove Tenderloin from smoker and tent with foil. Allow to rest (Minimum 20 minutes).