Preheat oven to 425°F. Combine 2 teaspoons thyme and garlic. Press evenly onto all surfaces of beef Roast. Place roast on rack in shallow roasting pan. Do not add water or cover. Toss bell pepper strips and tomatoes with oil, remaining 1 teaspoon thyme and salt on rimmed baking sheet.
Roast beef in 425°F oven 30 to 40 minutes for medium rare; 40 to 50 minutes for medium doneness. Roast pepper mixture in oven with roast 30 to 40 minutes or until vegetables are tender and begin to brown, stirring once.
Remove roast when instant-read thermometer registers 135°F for medium rare; 150°F for medium. Transfer roast to carving board; tent loosely with aluminum foil. Let stand 10 to 15 minutes. (Temperature will continue to rise about 10°F to reach 145°F for medium rare; 160°F for medium).
Meanwhile, combine mayonnaise and basil paste; spread evenly onto cut surfaces of rolls. Carve roast into thin slices; season with salt and pepper, as desired. Top each roll evenly with beef, pepper mixture, cheese and arugula. Close sandwiches.
Nutrition information per serving: 444 Calories; 144 kcal Calories from fat; 16 g Total Fat; 4 g Saturated Fat; 5 g Monounsaturated Fat; 74 mg Cholesterol; 689 mg Sodium; 44 g Total Carbohydrate; 3.6 g Dietary Fiber; 33 g Protein; 4 mg Iron; 13.1 mg Niacin; 0.7 mg Vitamin B6; 1.3 mcg Vitamin B12; 4.5 mg Zinc; 27.4 mcg Selenium; 93.7 mg Choline;