Melt two tablespoons butter and cook onions and green pepper in it until softened. Remove to a bowl. Stir chopped chicken and green chilis into onion-pepper mixture. Melt remaining 3 tablespoons of butter. Blend in flour and seasonings. Whisk in chicken broth. Cook, stirring, until sauce boils. Remove from heat; stir in sour cream and 1/2 cup cheese. Stir 1/2 cup sauce into chicken mixture.

Dip each tortilla in remaining hot sauce to soften and spoon chicken mixture into center of tortilla. Roll up and arrange in 13 x 9 x 2 inch pan; repeat with all tortillas. Pour remaining sauce over tortillas. Sprinkle with remaining cheese. Bake uncovered at 350 degrees for about 25 minutes.