1. Rinse and drain fennel. Trim tops, discard tough stalks, and save feathery greens. Coarsely chop enough greens to make 1/2 cup; save extras for garnish. Trim and discard root ends and bruised areas from fennel heads. Using a slicer, cut fennel into 1/16-inch-thick pieces.
2. In a 10- to 12-inch frying pan over high heat, mix fennel, garlic, oil, and 1/4 cup water. Stir often until liquid evaporates and fennel is lightly browned, about 6 minutes. Stir in 1/2 cup fennel greens and chilies. Remove from heat.
3. Wipe roast with a damp towel. With a paring knife, make a cut the length of the roast and parallel to the backbone to create a pocket that is about 3 inches deep. Spoon fennel mixture evenly into the pocket, packing it in to use all.
4. With cotton string, tie roast crosswise at every rib to hold fennel stuffing in place. Set meat, rib side down, on a rack in an 11- by 17-inch pan.
5. Bake at 375° until a thermometer inserted in the center of the thickest part registers 150° to 155°, about 2 1/4 hours.
6. Transfer roast to a platter; snip string and remove. Skim and discard fat from roast drippings. Scrape drippings free with 2 to 3 tablespoons water, and pour over meat. Garnish roast with reserved fennel greens. Slice between ribs to serve. Add salt and pepper to taste.