Preheat oven to 425°F. Combine 1 teaspoon salt, 1 teaspoon pepper and garlic; press evenly onto all surfaces of beef roast. Place roast on rack in shallow roasting pan. Insert ovenproof meat thermometer so that tip is centered in thickest part of beef, not resting in fat. Do not add water or cover.
Lightly coat Brussels sprouts with nonstick cooking spray. Add remaining 1/2 teaspoon salt and remaining 1/2 teaspoon pepper; toss to coat. Arrange Brussels sprouts around roast in roasting pan.
Roast 425°F oven for 40 to 50 minutes for medium rare; 50 to 60 minutes for medium doneness. Remove roast when meat thermometer registers 135°F for medium rare, 150°F for medium. Transfer roast to carving board; tent loosely with aluminum foil. Let stand 15 to 20 minutes. (Temperature will continue to rise about 10°F to reach 145°F for medium rare, 160°F for medium.) Brussels sprouts should be crisp around the edges and tender. Carve roast into slices. Serve with Brussels sprouts.