Soak corn husks in a bowl of warm water until softened, about 1 hour; drain.

Mix masa, 1 tablespoon paprika, 1 tablespoon chili powder, garlic powder, 1 teaspoon cumin, and 1 teaspoon salt together in a bowl. Stir corn oil into masa mixture. Measure 1/2 cup turkey broth and set aside. Add remaining broth, 1 cup at a time, to masa mixture until dough is smooth and the consistency of thick peanut butter.

Heat olive oil in a skillet over medium heat; saute onion and garlic until softened and translucent, 5 to 10 minutes. Remove skillet from heat and add turkey, 1 teaspoon paprika, oregano, 1 teaspoon cumin, 1 teaspoon chili powder, 1 teaspoon salt, black pepper, and cayenne pepper. Stir reserved 1/2 cup turkey broth into filling until moistened.

Spoon 1 heaping tablespoon dough in the center of each corn husk. Top filling with 1 heaping tablespoon filling. Roll husk around dough and filling, tucking bottom of husk into tamale. Tie a corn husk strip or string around each tamale to secure.

Place a steamer insert into a saucepan and fill with water to just below the bottom of the steamer. Bring water to a boil. Stand tamales upright in steamer, cover, and steam until cooked through, about 1 hour. Add more water as needed.