Heat a large cast-iron skillet over medium heat. Add beef, green chiles, hot sauce, salt, 3 cloves garlic, onion, black pepper, and cayenne pepper. Cook and stir until beef is thoroughly browned, 10 to 15 minutes. Drain and reserve the drippings.

Combine reserved drippings, masa, lard, and baking powder in a large bowl. Mix well. Add up to 1 cup water, 1 teaspoon at a time, until mixture is as thick as biscuit dough. Divide into 50 equal balls. Place dough balls between 2 cutting boards each lined with a sheet of waxed paper; flatten into circles.

Place each dough circle into a corn husk. Spoon about 3 tablespoons beef mixture in a line across the middle of each husk. Top with a small amount of cheese. Fold opposing sides of the tortilla to overlap the filling. Roll the husk around the tamale and fold in one end.

Combine the remaining 1 clove garlic, 1 cup water, and chili powder in a small saucepan over medium-high heat. Bring chili sauce to a boil. Remove from heat.