Preheat oven to 325°F. Coarsely chop 3 slices bacon. Combine bacon, 1 tablespoon tarragon and 3 cloves garlic; press evenly onto all sides of beef Roast.
Place roast, fat-side up, 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 325°F oven 1 to 1-1/4 hours for medium rare; 1-1/4 to 1-1/2 hours for medium doneness.
Meanwhile, chop remaining slice bacon. Cook bacon in large nonstick skillet 3 to 5 minutes or until bacon is browned and crisp, stirring occasionally. Remove with slotted spoon to paper-towel-lined plate, reserving drippings in skillet. Add carrots, parsnips, 3/4 cup water and remaining clove garlic to same skillet. Bring to a boil. Reduce heat and simmer, covered, 10 minutes, stirring occasionally. Remove cover and continue cooking 2 to 4 minutes or until water has evaporated and vegetables are crisp-tender, stirring occasionally. Season with salt and pepper, as desired. Keep warm; set aside.
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 10 to 15 minutes. (Temperature will continue to rise about 10°F to reach 145°F for medium rare; 160°F for medium.)
Sprinkle vegetables with reserved bacon and remaining 1 tablespoon tarragon. Carve Roast into slices; season with salt and pepper, as desired. Serve with vegetables.