Sear the beef. Pat the beef pieces dry with a paper towel and season liberally all over with salt and pepper. Heat a 6 quart dutch oven over medium-high heat. Add the oil to the pot and once the oil is hot, arrange the beef pieces in a single layer. Sear for 4-5 minutes per side, until deeply browned. Transfer the beef to a plate.
Preheat an oven to 325 F.
Build the sauce. Lower the heat to medium and add the onion, garlic, and tomatoes. Cook for 3-4 minutes, until the onion is soft. Add the dried chilies, cumin, oregano, cinnamon, bay leaves, vinegar, bouillon, and water and stir well. Simmer for 10 minutes.
Blend the sauce. Use a slotted spoon to transfer the onion, garlic, tomato, chilies, and bay leaves to a high-powered blender (all the solids, basically). Add 2 cups of the cooking liquid to the blender and blend until very smooth. Return the pureed sauce to the pot and season well with salt and pepper. Nestle the beef into the sauce and cover with a lid.
Braise the birria. Transfer the pot to the oven and braise for 3 hours, or until the beef is very tender and shreds easily with a fork. Remove the pot from the oven and let the beef rest in the juices for 20 minutes.
Shred the beef. Transfer the beef from the pot to a cutting board or plate. Use a large spoon to skim the fat from the top of the braising liquid (be sure to save it if you’re making quesabirria tacos!). Set aside some of the braising liquid for tacos as well. Shred the beef and stir in a cup or two of the braising liquid and serve it as a stew topped with cilantro, onion, and radish. Serve with warmed tortillas and lime wedges on the side.