Preheat oven to 350 degrees. Combine chili powder, fennel seed, 1 teaspoon salt, and 3/4 teaspoon pepper and rub all over brisket. In a large heavy ovenproof pot, heat oil over medium-high. Cook brisket until browned on all sides, about 8 minutes total. Transfer to a plate.
Add onion to pot and saute 5 minutes. Stir in garlic and tomato paste and saute 1 minute. Add beer and 2 cups water, scraping up browned bits with a wooden spoon. Bring to a boil; return brisket to pot, cover, and transfer to oven. Braise until brisket is almost tender, about 3 hours. Tilt pot and spoon off fat from liquid. Add potatoes, carrots, and 1 cup water; braise until meat is very tender, 50 minutes more. Transfer brisket to a cutting board and let rest 10 minutes, then slice. Stir vinegar and cilantro into vegetables; serve with meat, sprinkled with more cilantro.
Brisket is a large, flat cut from the front end of the steer. You'll see two types at the supermarket. The so-called first cut, at left, is thinner and leaner than the thicker, marbled point, or second cut. Both will work here.