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1. In a large pot, add the beef chuck roast and beef shank. Season generously with salt and pepper.
2. Add the quartered onion and minced garlic to the pot.
3. In a dry skillet over medium heat, toast the guajillo and ancho chiles for about 2-3 minutes until fragrant.
4. Transfer the toasted chiles to a blender. Add the chipotle pepper, cumin, oregano, smoked paprika, and 1 cup of beef broth. Blend until smooth.
5. Pour the blended mixture over the beef in the pot. Add the remaining beef broth and water. Stir to combine.
6. Bring to a boil over medium-high heat, then reduce to low. Cover and simmer for 2-3 hours, or until the beef is fork-tender, stirring occasionally and adding more water if necessary.
7. In a separate pot, bring water to a boil. Add the ramen noodles and cook according to package instructions (about 3-4 minutes).
8. Drain the noodles and rinse under cold water to stop cooking. Set aside.
9. Remove the beef from the pot and let cool slightly. Shred using two forks, discarding large pieces of fat.
10. Strain the broth through a fine-mesh sieve into a large bowl or pot to remove solids.
11. Return the strained broth to the pot and bring back to a simmer. Adjust seasoning with salt and pepper as needed.
12. In serving bowls, add a portion of cooked ramen noodles.
13. Top with shredded beef and pour hot birria broth over the noodles and beef.
14. Garnish with chopped cilantro, diced onion, sliced radishes, shredded cheese, and avocado slices.
15. Serve with lime wedges on the side.

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