In 2-quart saucepan, melt butter over medium heat. Add onion; cook 3 to 5 minutes, stirring frequently, until tender. Reserve 1/4 cup enchilada sauce; add remaining sauce to onion. Stir in cumin and chicken. Reduce heat to medium-low; simmer uncovered 5 minutes.
Lightly grease 10-inch skillet with butter or cooking spray; heat over low heat. Place 1 tortilla in skillet; top evenly with pepper Jack cheese and second tortilla. Spread chicken mixture over second tortilla; top with third tortilla. Sprinkle evenly with Cheddar cheese; top with jalapeño chiles and green chiles. Place fourth tortilla over chiles; spread reserved 1/4 cup enchilada sauce over top.
Cover skillet; cook over low heat 18 to 20 minutes or until thoroughly heated. Remove from heat; let stand 10 minutes before serving. Cut into 4 wedges; serve topped with sour cream and if desired, several additional jalapeño chile slices.