Heat oven to 425°F. Combine thyme and pepper; reserve 1 tablespoon for mushrooms. Press remaining seasoning mixture evenly onto all surfaces of beef roast.
Place roast on rack in shallow roasting pan. Insert ovenproof meat thermometer so tip is centered in thickest part of beef, not resting in fat. Do not add water or cover. Roast in 425°F oven 35 to 40 minutes for medium rare; 45 to 50 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.)
Meanwhile melt butter in large nonstick skillet over medium heat. Add mushrooms and 1 tablespoon reserved seasoning; cook and stir about 7 minutes or until mushrooms are tender. Season with salt and pepper, as desired. Keep warm.
Carve roast into slices. Serve over grits, as desired; top with mushrooms.