In a large bowl, combine the masa harina, softened butter or lard, baking powder, and salt.
Gradually add the chicken broth, mixing until the dough is smooth and pliable. Adjust the consistency with more broth if necessary.
In a large skillet, heat the vegetable oil over medium heat. Add the ground pork or chicken and cook until browned, breaking it up with a spoon.
Add the chopped onion and minced garlic. Cook until the onion is softened.
Stir in the tomato sauce, green olives, capers, ground cumin, paprika, dried oregano, black pepper, and salt. Cook for another 5 minutes, or until the filling is well combined and heated through. Remove from heat and let cool slightly.
Drain the soaked corn husks and pat them dry.
Lay a corn husk flat and spread about 2 tablespoons of tamale dough in the center, leaving about 1 inch on each side.
Place a spoonful of the filling on top of the dough.
Fold the sides of the corn husk over the filling, then fold up the bottom to enclose the tamale. Secure with a strip of husk or kitchen twine if needed.
Place the tamales upright in a large steamer. Steam over simmering water for 1 to 1.5 hours, or until the masa is firm and cooked through. Add more water to the steamer as needed to keep the tamales moist.
Allow the tamales to cool slightly before serving.
Enjoy your meal!