Melt butter in a large skillet over medium-high heat, stirring often; add sliced onions, and cook 20 minutes or until caramelized. Reduce heat to low, and add chopped chicken and next 4 ingredients, stirring until combined. Set aside.
Pulse chiles and next 5 ingredients in blender or food processor several times until combined.
Bring chile mixture and chicken broth to a boil in a saucepan over high heat; cook 5 minutes or until slightly thickened. (Mixture should be the consistency of a thin gravy.) Remove from heat, and stir in salsa.
Spread one third chile mixture evenly on bottom of a lightly greased 13- x 9-inch baking dish.
Spoon chicken mixture evenly down center of each tortilla; roll up, and place, seam side down, in prepared baking dish. Top with remaining chile mixture; sprinkle with cheese.
Bake at 375° for 20 to 25 minutes or until bubbly.
Note: Freeze chile mixture and filled tortillas separately up to 1 month, if desired. Thaw in refrigerator overnight. Prepare and bake as directed.
To lighten: Substitute 1/3-less-fat cream cheese, 2% reduced-fat Cheddar cheese, and fat-free tortillas.