Pat and season the beef. Dry the beef with paper towels.
Season all sides with salt and black pepper. This helps with browning and flavor.
Sear for flavor. Heat olive oil in a heavy pot or Dutch oven over medium-high. Sear the beef on all sides until nicely browned, about 3–4 minutes per side.
Work in batches if needed. Transfer to a plate.
Build the base. Reduce heat to medium. Add onion and cook until softened and lightly golden, 5–7 minutes.
Stir in garlic, chili powder, cumin, smoked paprika, oregano, and cayenne. Cook 30 seconds until fragrant.
Deglaze and enrich. Stir in tomato paste and cook 1 minute. Add beef broth and scrape up browned bits.
Add bay leaf if using.
Simmer until tender. Return beef and any juices to the pot. Bring to a gentle simmer, cover, and cook on low until the beef shreds easily with a fork, about 2.5–3 hours on the stovetop or 3–4 hours in a 300°F (150°C) oven.
Pressure cooker option. For a faster route, combine seared beef, aromatics, spices, and broth in a pressure cooker. Cook on high pressure for 50–60 minutes, then natural release 15 minutes.
Shred and reduce. Transfer the beef to a board and shred with two forks.
Meanwhile, simmer the cooking liquid uncovered for 5–10 minutes to concentrate. Remove the bay leaf, then stir the shredded beef back in.
Brighten with lime. Off the heat, stir in fresh lime juice. Taste and adjust salt, pepper, and heat.
Add more lime if you want extra zing.
Assemble the bowls. Spoon rice or your chosen base into bowls. Top with a generous scoop of chili-lime beef. Add toppings like avocado, cabbage, beans, corn, tomatoes, and a dollop of sour cream.
Finish with cilantro and lime wedges.
Serve. Enjoy warm. The flavors deepen even more the next day.