This stout-braised lamb is most delicious made at least one day and up to three days ahead. If making the same day, skim excess fat from surface of braising liquid with a spoon.
Preheat oven to 325 degrees. Season lamb generously with salt and pepper. Sprinkle evenly with flour. Heat oil in a braiser pan or large deep-sided skillet over medium-high. Working in 2 batches, sear lamb, fat-side down first, until browned all over, 5 to 7 minutes a batch. Transfer to a platter.
Reduce heat to medium. Add onion to pan and cook, stirring occasionally, until softened, 5 to 6 minutes. Stir in garlic, rosemary, and tomato paste. Cook, stirring, until fragrant, about 1 minute.
Add Worcestershire, stout, and broth. Bring to a boil, scraping up browned bits from bottom of pan. Return lamb, fat-side up, and any accumulated juices to pan and return to a boil.
Cover pan and transfer to oven. Cook, spooning juices over lamb every 30 minutes, until meat is fork-tender, 2 1/2 to 3 hours. Remove from oven; uncover and let cool completely. Cover and refrigerate at least 1 day and up to 3 days.
Remove solidified fat from top. Place pan over medium-low and gently simmer, covered, until lamb is warmed through, about 15 minutes. Remove rosemary. Using 2 forks, shred meat into large pieces. Transfer to a tureen or other serving vessel. Pour braising liquid over lamb. Serve with jam or chutney.