Heat oven to 350°F. Prepare and bake gingerbread mix as directed on package using water and egg. Remove from pan; place on wire rack. Cool 1 1/2 hours or until completely cooled.
Meanwhile, in medium saucepan, combine brown sugar, cornstarch and cinnamon; mix well. Add cranberry juice and cranberries. Cook over medium heat until bubbly, thickened and most cranberries have popped, stirring constantly. Place plastic wrap on surface of cranberry mixture; set aside.
In medium bowl, prepare pudding mix as directed on package using milk. In small bowl, beat whipping cream until soft peaks form. Fold 1 cup of the pudding into whipped cream. Reserve remaining pudding.
Cut gingerbread into 1-inch cubes. Arrange 1/3 of gingerbread cubes in bottom of clear glass 2 1/2-quart soufflé dish or trifle bowl. Top with half of the peach slices; spoon half of cranberry mixture over peaches. Top with another 1/3 of gingerbread. Top with remaining peaches; spoon reserved pudding over peaches. Top with remaining gingerbread. Press lightly to compact layers. Spoon remaining cranberry mixture over gingerbread. Top with whipped cream-pudding mixture. Refrigerate at least 3 hours or overnight before serving.