Preheat oven to 350 degrees F (175 degrees C). 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 cup butter, 2 cups sugar, applesauce, and eggs. Mix in 1/2 cup 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 cup butter, and 1/3 cup 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.