01 - Heat vegetable oil in a large skillet over medium heat. Add the chopped onion and sauté until translucent, about 3 minutes. Stir in minced garlic and cook for 1 minute. Incorporate roasted green chiles, shredded chicken, ground cumin, dried oregano, salt, and black pepper. Pour in chicken broth, reduce the heat, and simmer for 10 minutes until most of the liquid is absorbed. Set aside to cool.
02 - In a large mixing bowl, beat the lard or vegetable shortening using an electric mixer or sturdy spoon until light and airy. In a separate bowl, combine masa harina, baking powder, and salt. Gradually add the masa mixture and warm chicken broth to the whipped lard, blending until a smooth, spreadable dough forms. The dough is ready when a small snippet floats in cold water.
03 - Drain the soaked corn husks and pat them dry. Spread approximately 1/4 cup of masa evenly onto the wide end of each husk, leaving a 1-inch border at the sides. Spoon 2 to 3 tablespoons of chicken filling into the center. Fold the sides of the husk over the filling, then fold up the narrow end to secure. Use a thin strip of corn husk to tie and keep the tamale closed if desired.
04 - Arrange the tamales upright in a steamer basket with the open ends facing upward. Pour water beneath the steamer basket, ensuring it does not touch the tamales. Cover with a damp towel and the lid. Steam for 1 1/2 to 2 hours, adding additional water as necessary, until the masa easily separates from the husk.
05 - Allow the tamales to rest for 10 minutes before plating. Remove the corn husks and serve hot with salsa or crema, as desired.