Preheat the oven to 350 degrees and grease a 9×13-inch baking dish. In a medium mixing bowl, prepare the crumb layer by mixing the melted butter, brown sugar, cinnamon, and flour until well combined. Set aside.
In a separate large bowl or the bowl of a stand mixer with a paddle attachment, add the oil, cane sugar, and brown sugar, blending until smooth.
To the sugar mixture, add the eggs, vanilla, sourdough starter, pumpkin, and milk, then mix well.
In a smaller bowl, stir the flour, pumpkin spice, baking soda, baking powder, and salt until combined. Add these dry ingredients to the wet ingredients, stirring until combined and smooth.
Pour half of the pumpkin batter into the prepared baking dish. Sprinkle half of the crumb mixture evenly on top. Pour the remaining cake batter over the top, then sprinkle the rest of the crumb mixture evenly.
Bake in the preheated oven for 40-50 minutes. The edges will turn golden, and a toothpick inserted should come out clean. Let cool before slicing and serving.
