Remove short ribs from fridge 30 minutes before cooking. Pat dry, trim fat caps thicker than ¼-inch, and season all sides with salt and pepper.
Preheat oven to 325°F. Heat oil in Dutch oven over medium-high heat. Brown ribs in batches, 3-4 minutes per side, until deep golden-brown.
Reduce heat to medium. Cook onion 5-6 minutes until translucent. Add garlic and cook 1 minute. Stir in tomato paste and cook 2 minutes. Add cumin, oregano, and paprika; cook 30 seconds.
Add chipotle peppers, adobo sauce, beer, beef stock, lime juice, and bay leaves. Stir and scrape up browned bits. Bring to a simmer.
Nestle ribs in liquid (liquid should reach three-quarters up the sides). Cover and braise in oven for 2 hours. Uncover and cook 30-60 minutes until fork-tender.
Remove ribs from pot and rest 10 minutes. Shred meat with two forks, discarding bones and fat. Return shredded beef to braising liquid and keep warm.
Warm tortillas in a dry cast iron skillet 15-20 seconds per side until pliable and slightly charred. Stack in a clean towel to keep warm.
Spoon generous portions of shredded beef onto tortillas, allowing some sauce to soak in. Top with onion, cilantro, queso fresco, and avocado. Serve with lime wedges.