Fresh whipped cream or ice cream, for serving
Preheat the oven to 350 degrees F. Grease and flour one 9-inch springform pan.
For the batter: In a large mixing bowl, cream together the butter and granulated sugar with an electric mixer until light and fluffy. Add the eggs, one at a time, beating well after each addition. Mix in the vanilla. In a separate mixing bowl, whisk together the flour, baking powder and salt. Stir the dry ingredients into the butter and egg mixture. Mix just until combined (the batter will be thick) and set aside.
For the filling: In a second large mixing bowl, add the brown sugar, cinnamon, ginger, nutmeg, pumpkin puree and eggs and set aside.
For the topping: In a third mixing bowl, combine the flour, brown sugar, baking powder, cinnamon, nutmeg and ginger. Cut in the chilled butter with a pastry cutter or two forks until the mixture is crumbly.
Evenly spread the thick cake batter on the bottom of the prepared pan. Next, pour the pumpkin filling over the top of the cake batter and sprinkle the crumb topping on top of the filling. Bake until the filling is set and the topping is golden brown, 1 1/2 to 2 hours. Cool before slicing. Serve with fresh whipped cream or ice cream.