Prepare the Pork : Place pork shoulder, onion, garlic, broth, cumin, salt, and pepper in a pot. Bring to a boil, then reduce heat and simmer for 1.5 hours or until pork is tender. Shred the pork using two forks. Reserve the cooking broth for the masa.
Make the Salsa Verde : Boil tomatillos, peppers, onion, and garlic in a pot until softened. Drain and transfer to a blender. Add cilantro, salt, and lime juice.
Blend until smooth. : Mix half of the salsa into the shredded pork. Reserve the rest for serving.
Prepare the Masa : Beat lard or shortening in a bowl until fluffy. Mix masa harina, baking powder, and salt in a separate bowl. Gradually add masa mixture to the lard while slowly adding warm pork broth. Mix until soft, spreadable, and light. Test by dropping a small ball of dough into water; it should float.
Assemble the Tamales : Drain corn husks and pat dry. Spread a thin layer of masa onto the center of each husk. Add 1–2 tablespoons of pork filling. Fold the sides of the husk inward, then fold the bottom up. Place tamales upright in a steamer pot.
Steam the Tamales : Add water to the bottom of the steamer without touching the tamales. Steam for 60–90 minutes. Tamales are done when the masa pulls away from the husk easily.