Soak the dried corn husks in warm water for at least 30 minutes until pliable. Drain and pat dry before using.
In a large skillet, heat the vegetable oil over medium heat. Add the chopped onion and minced garlic and sauté until softened and translucent, about 5 minutes.
Add the cooked shredded chicken, ground cumin, dried oregano, and salt to taste. Stir in 1 cup of the red chile sauce and cook for 5 minutes until well combined and heated through. Remove from heat and set aside.
In a large mixing bowl, combine the masa harina, baking powder, and 1 teaspoon salt. Gradually add the chicken broth and mix until a soft dough forms.
Using a hand mixer or by hand, beat the softened lard or vegetable shortening into the masa dough until the dough is light and fluffy, about 5 to 7 minutes.
Spread a thin layer (about 2 tablespoons) of masa dough onto the center of each soaked corn husk, leaving about 1 inch at the bottom and sides.
Place about 2 tablespoons of the chicken filling in the center of the masa layer on each husk.
Fold the sides of the husk in toward the center, then fold the bottom up to enclose the filling securely. Tie with thin strips of soaked husk if needed to keep tamales closed.
Arrange the tamales upright in a large steamer pot with the open ends facing up. Add water to the bottom of the steamer, making sure it does not touch the tamales.
Cover the tamales with a damp kitchen towel and the steamer lid. Steam over medium heat for 1 hour and 30 minutes, adding more water as needed to maintain steam.
Check for doneness by peeling back a husk; the masa should be firm and easily pull away from the husk.
Remove tamales from the steamer and let cool for 10 minutes before serving.