Heat oven to 350°F. Make pie crusts as directed on box for Two-Crust Pie using 9-inch glass pie plate. In small bowl, beat cream cheese, goat cheese, granulated sugar and vanilla with electric mixer on high speed until smooth. Spread in crust-lined plate; top with banana slices.
In 1-quart saucepan, heat butter, brown sugar, cinnamon and nutmeg over low heat, stirring constantly, until butter is melted and mixture is smooth. Remove from heat; stir in rum extract. Pour over bananas. Top with second crust and flute; cut slits in several places. Brush with milk; sprinkle with coarse sugar.
Cover edge with strips of foil to prevent excessive browning; bake 30 minutes. Remove foil; bake 30 to 40 minutes longer or until golden brown. Cool at least 2 hours before serving. Store covered in refrigerator.