Preheat the oven to 375°F (190°C).
In a medium pot over medium heat, combine the softened cream cheese and both cans of cream of chicken soup; stir until smooth and warmed through.
Stir in the Italian dressing mix, then reduce the heat to low and keep a small amount warm in the pot to use as gravy later.
Transfer most of the creamy mixture to a large bowl, leaving a few spoonfuls in the pot for topping.
Add the shredded cooked chicken and chopped green onions (if using) to the bowl and mix until evenly combined.
Separate the crescent roll dough into individual triangles and place them on a baking sheet.
Spoon about one portion of the chicken mixture onto the wide end of each crescent triangle. Fold the shorter sides in over the filling, then roll toward the point to form a bundle.
Arrange the bundles on the baking sheet and bake for 9–12 minutes, until the crescent rolls are golden brown.
Remove from the oven and, if desired, spoon the reserved warm gravy over the bundles before serving.
