Place chicken in a greased 2-qt. baking dish; cover with water. Cover and bake at 350° for 30 minutes or until a thermometer reads 170°.
Meanwhile, in a small skillet, saute mushrooms and onion in butter until tender. Combine cornstarch and milk until smooth; stir into skillet. Add seasonings. Bring to a boil; cook and stir for 2 minutes or until thickened.
Drain chicken. Cut pastry sheets in half widthwise. On one side of each half, place a chicken breast, 1/4 cup mushroom mixture, two ham slices and one cheese slice. Fold pastry over filling and seal edges.
Place on a greased baking sheet. Brush tops with milk if desired. Bake at 400° for 15-20 minutes or until puffed and golden.