Place corn husks in a large bowl and cover with boiling water. Allow to soak for 30 to 60 minutes. Drain, place husks on a work surface, and cover with a clean, damp towel.
While husks are soaking, line a heavy cast iron grill pan or griddle with aluminum foil and place it over high heat. Arrange poblano peppers in a single layer over foil. Grill until peppers are blackened, turning as necessary, 3 to 5 minutes. Transfer to a resealable plastic bag and let them steam, 10 to 15 minutes. Peel off skins and remove seeds. Cut into strips and set aside.
Place tomatillos in a medium pot and cover with water; bring to a boil. Cook until tomatillos change color, about 5 minutes. Drain, place in a blender, and blend until smooth. Set sauce aside.
Heat 1 tablespoon lard in a large pot over medium heat. Cook and stir onion in hot lard until soft and translucent, about 5 minutes. Add blended tomatillos; season with salt and pepper. Bring to a boil, reduce heat, and simmer until flavors are well combined, about 5 minutes. Add poblano pepper strips and cilantro; cook at a boil for 5 minutes. Remove from heat and allow to cool, about 10 minutes.
Beat remaining lard in a large bowl with an electric mixer until creamy. Season with salt and continue beating for a few minutes. Beat in masa harina and baking powder until well combined. Mix in broth, 1/4 cup at a time, until dough has a smooth and workable consistency that is not too wet, similar to cookie dough. Test if masa mixture is ready by dropping a small ball of masa into a glass of cold water; if it floats, it's ready; if not, keep working dough a little longer.
Select 1 wide corn husk or 2 small ones. Spread about 2 tablespoons masa mixture onto corn husk, filling it 2 inches from the bottom and 1/4 inch from the top. Add 1 tablespoon tomatillo sauce and a Monterey Jack cheese slice in the center of masa mixture. Fold the sides of husk together, one over the other. Fold the bottom of the husk over the seam of the 2 folded sides. Repeat with remaining husks.
Place a steamer insert into a saucepan and fill with water to just below the bottom of the steamer. Bring water to a boil. Place tamales, open-side up, into the insert. Cover and steam until filling is heated through and separates from husk, about 1 hour 15 minutes. Let tamales rest for 15 minutes before serving.