Cook bacon in a heavy 5- to 6-qt. pot over medium heat. Transfer bacon to a large bowl. Pour off all but 1 tbsp. bacon fat from pot, add 1 tbsp. oil, and cook larger sliced mushrooms until beginning to crisp on edges, about 10 minutes; transfer to a second bowl.
Dry beef on paper towels if wet, then season with 1 tsp. salt and the pepper. Add another 1 tbsp. oil to pot. Brown meat in 3 batches over medium-high heat until nicely browned all over, 20 to 30 minutes total. Add meat to bacon.
Add remaining 1 tbsp. oil and flour to pot. Cook over medium heat, stirring often, until flour is a shade darker, 2 to 4 minutes. Stir in remaining 1 1/2 tsp. salt, the thyme, allspice, and tomato paste. Pour in ale and broth; scrape up any browned bits from bottom of pot. Add reserved beef and bacon and accumulated juices. Bring to a boil, covered, then reduce heat to maintain a gentle simmer.
Simmer, stirring occasionally, 1 1/2 hours. Meanwhile, peel shallots and separate into lobes. Peel carrots and cut into 1- by 1/2-in. sticks.
Add shallots, cooked and raw mushrooms, potatoes, and carrots to beef and simmer, covered, 1 hour, or until beef is meltingly tender. Sprinkle with chives.
*Find at farmers' markets and well-stocked grocery stores.
TIPS FOR COOKS Shop: Regardless of variety, all mushrooms should smell sweet and earthy and have dry, firm, undamaged caps. If they're spongy or sticky, steer clear. Store: Keep in a paper bag (storing them in plastic rots them), chilled, up to 4 days. Even if they become completely dry, they'll be fine in stews; the juices plump them back up. Clean: Wipe with a barely damp paper towel. If they're very dirty or sandy, swish briefly in cold water and scrub with a small brush, then dry immediately (they get soggy fast). To cook or not to cook?: Most experts advise cooking all edible mushrooms because, to varying degrees (and depending on the person), they're difficult to digest raw. Also, many have toxins that cooking destroys. However, there's no conclusive proof that eating mild raw mushrooms, especially in moderation, is harmful.
* Percent Daily Values are based on a 2,000 calorie diet. Your daily value may be higher or lower depending on your calorie needs.