Pat beef chunks dry with paper towels. Season all over with 1 teaspoon salt and the pepper. Heat 1 tablespoon oil in a large Dutch oven over medium-high heat. Working in batches, sear beef until deeply browned on all sides, about 3-4 minutes per side. Transfer to a plate and set aside.
Reduce heat to medium. Add remaining 1 tablespoon oil to the pot. Add diced onion and cook until softened and translucent, about 4-5 minutes. Stir in garlic and cook for 30 seconds until fragrant.
Add minced chipotle peppers, adobo sauce, cumin, oregano, smoked paprika, and remaining ½ teaspoon salt. Cook for 1 minute, stirring constantly, until spices are toasted and aromatic. Pour in beef broth and add bay leaf. Bring to a simmer, scraping up any last bits from the bottom.
Return seared beef and any accumulated juices to the pot. Liquid should come about halfway up the meat; add a little water if needed. Bring to a gentle simmer, then cover and reduce heat to low. Cook for 2.5 to 3 hours, or until beef is fork-tender and reaches an internal temperature of at least 145°F (63°C); for easy shredding, aim for 195°F (90°C).
Transfer beef to a cutting board (reserve braising liquid in pot). Use two forks to shred meat into bite-sized pieces, discarding any large fat pieces. Return shredded beef to the pot and toss with the reduced sauce. Simmer uncovered for 10 minutes to concentrate flavors if needed.
Warm corn tortillas on a dry skillet or directly over gas flame until pliable and slightly charred. Fill each tortilla with shredded beef, then top with diced onion, fresh cilantro, a squeeze of lime, and your favorite salsa. Serve immediately.