In a large pot, add the beef chuck roast, beef shank, chopped onion, minced garlic, and enough beef broth and water to cover the meat. Bring it to a gentle simmer over medium heat. Allow it to cook for about 3 hours until the beef is tender and easily shreds with a fork. Skim off any excess fat from the surface for a cleaner broth.

Remove the beef from the pot and set it aside to cool. In the same pot, add the dried guajillo and ancho chiles. Simmer them in the broth for about 10 minutes until they soften. Transfer the chiles and broth to a blender, and blend until smooth. Strain the mixture back into the pot, discarding the solids, to create a rich, flavorful broth for your Birria Ramen.

Once the beef has cooled slightly, use two forks to shred it into bite-sized pieces. Return the shredded beef to the pot with the strained broth. Stir to combine and let it simmer on low for an additional 15 minutes, allowing the flavors to meld beautifully. The beef should be incredibly tender, ready to be enjoyed in your ramen.

In a separate pot, bring water to a rolling boil and cook the ramen noodles according to package instructions, usually about 3-5 minutes for fresh noodles. Drain the noodles and rinse them briefly under cold water to prevent them from sticking. Set them aside, ready to absorb the delicious broth of the Birria Ramen.

To serve, place a generous amount of the cooked ramen noodles at the bottom of each bowl. Ladle the hot, spiced broth over the noodles, making sure to add a decent portion of the tender beef.

Finish your dish by adding a sprinkle of freshly chopped cilantro, diced onions, and avocado slices on top of the hearty bowl. Include sliced radishes for an extra crunch and a handful of shredded cheese for creaminess. Serve each bowl with lime wedges on the side to squeeze in a burst of freshness and acidity just before indulging.