Preheat oven to 450 degree F. In a food processor, combine fennel, snipped rosemary, garlic, salt, pepper, and 1 tablespoon of the olive oil. Cover and process to make a chunky paste.
Untie roast. Spread half of the fennel mixture on the inside of the loin. Roll tightly and tie with 100-percent-cotton kitchen string. Thread the 2 sprigs of rosemary through the ties on either side of the roast. Make holes in the top and sides of the roast with a skewer; brush remaining 1 tablespoon oil over the roast. Spread remaining fennel mixture over the roast. Place roast on a rack in a shallow roasting pan.
Roast in the preheated oven, uncovered, for 15 minutes. Turn oven temperature down to 400 degree F; drain fat from the pan and place the vegetables around the roast. Roast for 15 minutes more. Add broth to pan. Roast 50 to 60 minutes more or until a meat thermometer registers 155 degree F, pouring broth over meat a little at a time every 15 to 20 minutes.
Remove the roast to a platter; cover with foil and let stand 15 minutes before carving. Pass vegetables and pan juices through a sieve or food mill. Skim fat and cook sauce over medium heat a few minutes if it is too thin. Season with salt and pepper, if needed, and serve with the sliced roast. Makes 8 servings.