Flatten chicken breasts to 1/4-in. thickness. Place a slice of cheese on each; roll up and secure with toothpicks. In a shallow bowl, beat egg, water and mustard. In another shallow bowl, combine the bread crumbs, thyme, salt and pepper. Place flour in a third shallow bowl. Lightly coat chicken with flour, then dip in egg mixture and roll in bread crumb mixture.
In a large skillet, brown roll-ups in oil until golden brown, turning often. Transfer to an ungreased 13-in. x 9-in. baking dish. Bake, uncovered, at 350° for 20-25 minutes or until chicken juices run clear.
Meanwhile, drain cherries, reserving juice. Add enough water to juice to measure 1 cup. In a large saucepan, combine sugar and cornstarch. Stir in cherry juice until smooth. add cherries. bring to a boil; cook and stir for 2 minutes or until thickened. Remove from heat. Stir in lemon juice, extract and food coloring if desired.
Discard toothpicks. Serve with cherry sauce. Yield: 8 servings.