Prepare one-half batch of homemade tamale masa according to your preferred recipe or nixtamalization method, reducing the original quantities by half where necessary.
Place the dried corn husks in a large bowl or pot and completely cover them with hot water. Allow them to soak for 30–45 minutes, or until sufficiently soft and flexible for folding.
Transfer the softened husks to a colander and allow the excess water to drain. Soak several additional husks if possible, as these can be used to line the steaming rack.
Warm the vegetable oil in a medium saucepan over medium heat.
Add the finely diced white onion, chopped tomato, and minced garlic. Sauté for approximately 1 minute, just until the mixture becomes aromatic.
Add the roasted, peeled, and diced green chiles and stir until evenly distributed throughout the vegetable mixture.
Season with the kosher salt and black pepper, then pour in the chicken broth.
Allow the filling to gently simmer for 3–5 minutes so the ingredients and seasonings can combine thoroughly.
Taste the mixture and adjust the salt or pepper as necessary.
Reduce the heat to low. Add the shredded cheese and stir until completely melted and evenly incorporated. Remove the saucepan from the heat and reserve the filling for assembly.
Place one softened corn husk on the work surface with its smooth side facing upward.
Spoon approximately 1–2 generous tablespoons of prepared masa onto the center of the husk.
Using the back of a spoon, spread the masa into an oval layer while keeping a clear border around the edges of the husk.
Arrange approximately 1–2 generous teaspoons of the green chile and cheese mixture in a narrow line through the center of the masa.
Fold the two long sides of the corn husk inward so they overlap around the filling, then bring the narrow bottom end of the husk upward to close the tamal.
Place the completed tamal seam-side down. Repeat the process with the remaining masa, filling, and corn husks until all of the ingredients have been used.
Pour water into the bottom of a tamale steamer or a large pot fitted with a steaming rack. Keep the water level below the rack so the tamales do not sit directly in the liquid.
Place two clean pennies in the water if using this method to monitor the liquid level. They will rattle while sufficient water remains in the pot.
Cover the steaming rack with several of the extra soaked corn husks to help prevent the tamales from sticking.
Position the assembled tamales vertically in the steamer with their open ends facing upward.
Cover the pot and bring the water to a boil. Once boiling, reduce the heat to medium and steam the tamales for 45–60 minutes.
Check the water periodically during steaming and add additional hot water whenever necessary. If using the pennies as a water-level indicator, replenish the water if the rattling stops.
Test one tamal near the end of the cooking period by carefully removing and unwrapping it. The masa is ready when it holds its form and separates easily from the corn husk.
Carefully lift the cooked tamales from the steamer using tongs.
Allow them to stand for approximately 10 minutes before serving. This brief resting period gives the masa time to firm further, helping the tamales retain their shape and unwrap more cleanly.