Place husks in large pot or large bowl; add water to cover. Place heavy plate on husks to keep submerged. Let stand until husks soften, turning occasionally, at least 3 hours and up to 1 day - I find that over-night is perfect.
Preheat boiler. Line heavy baking sheet with foil. Arrange tomatillos on prepared sheet and broil until tomatillos blaken in spots, turning once (about 5 minute per side). Transfer tomatillos and any juices on sheet to processor and cool.
Add chiles and garlic to processor and blend until smooth puree forms.
Heat oil on medium sauce pan over medium-high heat. Add tomatillo puree and boil 5 minutes, stirring often.
Add broth and reduce heat to medium; simmer until sauce coats spoon thickly and is reduced to 1 cup, stirring occasionally, about 40 minutes.
Season with salt and mix in chicken and cilantro (can be made 1 day ahead, cover and chill).
I usually double this portion of the recipe and freeze half, it holds very well in the freezer.
Using electric mixer, beat shortening (with salt and baking powder if using) in large bowl until fluffy.
Beat in fresh masa or masa harina mixture in 4 additions.
Reduce speed to low and gradually beat in 1 1/2 cups broth, forming tender dough. If dough seems firm, beat in enough broth, two tablespoons at a time to soften.
Fill bottom of pot with steamer insert with enough water (about two inches) to reach bottom of insert. Line bottom of insert with some softened corn husks.
Tear 3 large husks into 1/4-inch-wide strips to use as ties and set aside. This isn't necessary, I only do it when I want to make the tamales look "pretty".
Open 1 large husks on work surface. Spread 1/4 cup dough in 4-inch square in center of each, leaving 2-3-inch plain border at narrow end of husk.
Spoon heaping tablespoon filling in strip down center of dough square. Fold sides of husk towards center and the narrow bottom end up so that the chicken mixture is "contained" in the center of dough and husk. This is where you can tie them with a strip of husk, but I find it isn't necessary. Leave wide end of tamale open.
Stand tamales in steamer basket, open end UP. Repeat with more husks, dough and filling until all filling has been used. If necessary, to keep tamales upright in steamer, insert pieces of crumpled foil between them.
Bring water in pot to boil, cover and steam tamales until dough is firm to touch and separates easily from husk, adding more water to pot as necessary, about 45 minutes.
Let stand 10 minutes.
Can be made 2 days ahead. Cool one hour, cover and chill. Before serving, re-steam tamales until hot, about 35 minutes.