Cake:
2 cups self-rising flour
3 teaspoons pumpkin pie spice
1 1/2 cups white sugar
1/2 cup light brown sugar, packed
1/2 cup vegetable oil
1/4 cup melted butter
1/2 cup unsweetened applesauce
1 1/2 teaspoons vanilla extract
3 cups unsweetened canned pumpkin puree
4 eggs, lightly beaten
Glaze:
1 (4 ounce) package cream cheese, softened
1 tablespoon butter, softened
2 cups confectioners' sugar
1 teaspoon rum extract
1 tablespoon milk

Preheat oven to 350 degrees F (175 degrees C). Grease and flour a Bundt cake pan.
Sift the flour and pumpkin pie spice together into a bowl. In another mixing bowl, beat the white and brown sugar, vegetable oil, butter, applesauce, vanilla, pumpkin, and eggs together until smooth. Gradually beat the flour mixture into the pumpkin mixture, 1/2 cup at a time, until completely smooth and well blended. Pour the batter into the prepared Bundt pan.
Bake in preheated oven until a wooden skewer inserted into the cake comes out clean. If not done, place a sheet of aluminum foil over the top of the pan, and bake 10 minutes more. Cool the cake in the pan 30 minutes before inverting onto a serving plate. Cool completely before glazing.
To make the glaze, mix the cream cheese with the butter, confectioners' sugar, rum extract, and milk in a bowl. Heat in a microwave oven for 15 seconds. Drizzle spoonfuls over the cooled cake. Refrigerate until ready to serve.