Meanwhile, heat oil over medium heat in a large pan. Add onion and garlic; cook and stir until soft, about 5 minutes. Add tomatoes and cook until they break down, about 5 minutes. Let the mixture cool.

Place peppercorns, cloves, dried ginger, cumin seeds, thyme, marjoram, and oregano in a mortar and grind into a fine mix.

In a blender, combine soaked chilies, 1/4 cup of the chile soaking liquid, onion-tomato mix, ground spices, chicken bouillon, and apple cider vinegar. Blend until smooth. Add a small amount of beef broth if needed for blending. Taste sauce; season with salt.

To cook meat, place chuck roast, beef shanks, and beef short ribs in a large pot and pour the sauce over it. Add enough beef broth to cover meat by about 1 inch, then stir to combine. Bring to a boil over high heat, then add cinnamon stick, onion, garlic, and bay leaves. Cover, and reduce heat to low, and simmer until meat is tender and falling apart, about 2 1/2 hours. Remove and discard short rib bones; skim fat from surface of broth using a spoon. Reserve fat for another use, such as quesabirrias. Taste broth; season with salt.

Bring a large pot of salted water to a boil, add ramen, and cook until tender, 7 to 20 minutes, or according to package instructions. Drain; divide noodles into bowls.

To assemble the dish, ladle birria and broth over ramen. Top with chopped onion and cilantro. Serve with lime wedges.