1Heat oven to 325°F. Grease and flour 12-cup fluted tube cake pan, or spray with baking spray with flour. In small bowl, beat cream cheese with electric mixer on high speed until smooth and fluffy. Beat in granulated sugar, 1 tablespoon flour, 1 egg, 1/8 teaspoon peppermint extract and 3 drops food color until smooth; set aside.
2In large bowl, beat cake mix, 1/3 cup flour, 1 cup water, the butter and 2 eggs on low speed 30 seconds, then on medium speed 2 minutes. Pour into pan. Spoon cream cheese filling over batter.
3Bake 44 to 52 minutes or until toothpick inserted in center of cake comes out clean. Cool in pan 15 minutes. Turn pan upside down onto cooling rack or heatproof plate; remove pan. Cool completely, about 1 hour.
4In 1-quart saucepan, heat chocolate chips and shortening over low heat, stirring frequently, until melted; set aside. For glaze, mix powdered sugar, 1/4 teaspoon peppermint extract, 1 to 2 drops food color, the corn syrup and enough of the 3 to 4 teaspoons water to make a thick glaze that can be easily drizzled. Drizzle over cake. Immediately spoon melted chocolate over glaze in 1/2-inch-wide ring. Working quickly, pull toothpick through chocolate to make swirls. Refrigerate until serving time. Store loosely covered in refrigerator.