Preheat oven to 325°F. Spray a 9x13-inch light-colored aluminum pan with nonstick cooking spray or line with parchment paper. Set aside.
In a large bowl, whisk together flour, baking powder, baking soda, salt, cinnamon, allspice, and nutmeg. Set aside.
In a separate large bowl, whisk together the brown sugar and granulated sugar. Add melted butter and oil, whisking until smooth and glossy.
Add eggs one at a time, whisking well after each addition.
Add sour cream and milk, stirring to combine.
Gradually add the dry ingredients to the wet ingredients, stirring until just combined. Do not overmix.
Pour the batter into the prepared pan and spread it into an even layer with a spatula.
Bake for 40-45 minutes, or until a toothpick inserted in the center comes out with a few moist crumbs, but no wet batter. If the top starts to brown too quickly, loosely tent the pan with foil around the 25-minute mark.
Remove the cake from the oven and place the pan on a wire rack to cool completely.*