Season the beef with salt and pepper. Sear in a large pot with a bit of neutral oil until browned on all sides; set aside.
Add the water to the same pot and bring to a boil. Add the chiles and tomatoes and simmer until soft, about 10 minutes.
Toast the spices (cumin, peppercorns, cloves, cinnamon, sesame, oregano) in a dry pan for about a minute then remove and set aside.
In the same pan, char the onion, garlic, and ginger briefly, then blend everything with the softened chiles and tomatoes plus 1 cup of the cooking liquid until smooth.
Pour the sauce through a strainer into the pot with the beef, add bay leaves, and simmer on low for 3–4 hours until tender.
Adjust seasoning with salt, pepper, and a pinch of sugar if needed.
Shred the beef finely and return it to the pot. Let the mixture simmer uncovered for 10-15 minutes so the broth reduces slightly and clings to the meat.
In a large bowl, beat the lard with a mixer for about 8-12 minutes until light and fluffy (it will look like marshmallow fluff).
In another bowl, whisk masa harina, baking powder, and salt.
Gradually add the dry ingredients to the lard, pouring in the warm birria broth a little at a time until the masa is smooth and spreadable, similar to peanut butter.
Mix in the birria fat for extra flavor. To check if it’s ready, drop a small piece into cold water — if it floats, you’re good to go.
Keep the masa covered with a damp cloth while you assemble.
Lay a soaked corn husk flat with the wide end at the bottom. Spread about 2-3 tablespoons of masa in the center, leaving space at the sides and bottom.
Add a heaping spoonful of birria and a strip of Oaxaca cheese.
Fold one side over, then the other, and fold the bottom up to seal and smear a little masa over the open side.
Repeat with the rest of the husks.
Stand them upright in a tamale steamer with the open ends facing up.
Add about 1½ inches of hot water to the bottom — don’t let it touch the tamales — and cover with a damp cloth and lid.
Steam for 1½ to 2 hours, checking every 30 minutes and adding more hot water as needed.
They’re done when the masa pulls away cleanly from the husk and feels firm.
Let the tamales rest for 10 minutes after steaming so they set.
Serve warm with chopped onion, cilantro, lime wedges, and a side of birria consomé for dipping.
