Sautee diced onion in a large pan with 2 Tbsp. butter. Remove from heat.  Add cream cheese. Stir until melted and mixed well with onions.  Add chicken and mix well again.Spoon a generous Tbsp of chicken mixture onto the wide end of each crescent roll.  Roll crescent roll towards point of roll and tuck in the sides.Place stuffed rolls about 1/2 inch apart in a 9x13 baking dish. (This recipe usually requires 2-3 baking dishes.)In a sauce pan or medium-low heat (or in the microwave) combine the cream of chicken soup, broth and milk.  Heat just until well combined.Pour sauce over rolls until rolls are covered.  Top with grated cheese.Bake at 350 degrees for 30 minutes or until golden and bubbly.