Preheat oven to 350F. Generously grease a 7 by 11-inch baking dish or an 8-inch pan, 9-inch pan, or 10-inch pan with butter. (You can use either round or square 8, 9, or 10-inch pans.)
Mix together all spices for the spice mix; set aside.
For the topping, whisk together the brown sugar, flour, half the spice mix (or 2 teaspoons 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 2 teaspoons 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 40 minutes. (Start checking it at 25 minutes; it will take more or less time depending on the size of your pan and whether your pan is glass or metal.)
Cool completely, and then sift the powdered sugar on top of the cake.
Notes
Pumpkin Spice Mix: Instead of making your own spice mix, you can use pumpkin pie spice mix instead; use 2 teaspoons pumpkin pie spice mix for the topping and 2 teaspoons pumpkin pie spice mix for the cake.
Baking Time: Like the recipe says, be sure to take this cake out of the oven when a toothpick comes out slightly moist with just a couple crumbs; it is perfect like this!