Preheat oven to 325F. Generously grease a 7 by 11-inch baking dish or 10-inch round pan with butter.
Mix together all spices for the spice mix; set aside.
For the topping, whisk together the brown sugar, flour, half the spice mix (or 1 3/4 teaspoon pre-made pumpkin pie spice mix), salt, and vanilla in a large bowl. Use a fork to cut the butter into the mixture, then once the dough forms pieces the size of peas, use your hands to work it until it forms large wet crumbs. Set aside.
For the cake batter, whisk together the oil, brown sugar, egg, pumpkin puree, and vanilla extract. Stir in the flour, baking powder, salt, baking soda, and the remaining half of the spice mix (or 1 3/4 teaspoon pre-made pumpkin pie spice mix); be careful not to over-mix.
Spread the batter out in the prepared pan and sprinkle on the crumble topping. Bake until a toothpick inserted in the center comes out slightly moist with just a couple crumbs, about 25 to 30 minutes.
Cool completely, and then sift the powdered sugar on top of the cake.