Combine 3/4 cup brown sugar, flour, and next 3 ingredients in a lightly greased 9- x 1 3/4-inch round cakepan.
Stir together milk, oil, and vanilla; add to sugar mixture, stirring until blended. Stir in apple. Sprinkle with remaining 3/4 cup brown sugar. Pour hot apple cider slowly over batter. Do not stir.
Bake at 350° for 30 to 35 minutes or until a cake layer forms on top. Cool slightly, and serve with ice cream.