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Toast the dried guajillo and ancho chiles in a dry skillet over medium heat for about 1 minute per side until fragrant and slightly puffed. Transfer to a bowl and cover with hot water. Let soak for 15-20 minutes until soft.
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Season the chuck roast chunks generously with salt and pepper. Heat vegetable oil in a large Dutch oven over medium-high heat. Sear the beef on all sides until deep golden brown, about 3-4 minutes per side. Work in batches so you don't crowd the pot. Remove beef and set aside.
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Drain the soaked chiles (save the soaking liquid). Add the chiles to a blender with the quartered onion, garlic, tomatoes, cumin, oregano, smoked paprika, cloves, apple cider vinegar, and about 1 cup of the chile soaking liquid. Blend until completely smooth.
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Pour the chile sauce through a fine mesh strainer into the Dutch oven (this removes any tough bits). Add the beef broth and seared beef. The liquid should mostly cover the meat — add more broth or water if needed. Bring to a boil, then reduce heat to low, cover, and simmer for 2.5 to 3 hours until the beef is fall-apart tender.
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Remove the beef from the pot and shred it with two forks. Taste the consomme broth and adjust salt as needed. Return the shredded beef to the pot to keep warm.
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Cook the ramen noodles according to package directions (discard the seasoning packets — you won't need them). Drain and divide among bowls. Ladle the birria consomme and shredded beef over the noodles. Top with fresh cilantro, diced onion, sliced radishes, and a squeeze of lime. Serve immediately.