Preheat oven to 350 degrees. Lightly grease a 9 inch Bundt pan. In a medium bowl, mix the flour, cocoa powder, pumpkin pie spice, baking powder and baking soda. In a large bowl, beat together 3/4 C. butter, 2 C. sugar, applesauce, and eggs. Mix in 1/2 C. heavy cream and pumpkin. Stir into the flour mixture just until blended. Spread evenly in the prepared pan. Bake 40 minutes in the preheated oven, or until a toothpick inserted into the center of the cake comes out clean. Allow to cool in the pan over a wire rack. Invert cake onto a serving plate.
Place the brown sugar, 1/2 C. butter, and 1/3 C. heavy cream in a medium saucepan. Bring to a boil while stirring to blend until smooth. Cook until sugar is dissolved. Whisk in the confectioner's sugar, and drizzle over the cake immediately.