Remove meat from chickens and coarsely shred, place in medium bowl (you will need 5-1/2 cups, reserve any extra for use another day). Discard skin and bones. Stir 1/2 cup salsa verde into chicken to evenly coat.
Preheat oven to 350 degrees. Grease two 9x13 glass or ceramic baking dishes, set aside.
In 12-inch skillet, heat remaining salsa verde, green onions, and lime juice to boiling on medium-high. Boil 2 minutes, stirring occasionally. Stir in 2 tablespoons cilantro, keep warm over very low heat.
With tongs, place 1 tortilla in salsa verde mixture, heat 10 seconds. Place tortilla on parchment paper, top with about 1/3 cup shredded chicken mixture. Roll up tortilla and place, seam side down, in prepared baking dish. Repeat with remaining tortillas and chicken mixture, arranging 8 tortillas in each dish.
Stir sour cream and broth into remaining salsa verde mixture in skillet, spoon over filled tortillas. Cover one baking dish with foil and bake 15 minutes. Remove foil, sprinkle with 1 cup cheese and 1 tablespoon cilantro. Bake 5 minutes longer or until cheese melts.
Meanwhile, sprinkle remaining cheese and cilantro over second casserole and prepare for freezing.
Cook's Note: I have used six 10-inch tortillas instead of eight 6-inch tortillas in each pan as pictured above.