Preheat the oven to 350°F (177°C). Spray a 9x13 baking pan well with nonstick cooking spray and set aside.
In a large mixing bowl, whisk together the flour, baking powder, baking soda, salt, and spices until well combined. Set aside.
In a separate large mixing bowl, whisk together the brown sugar, oil, applesauce, eggs, vanilla extract, and buttermilk until fully combined.
Add the dry ingredients to the wet ingredients and mix together until just combined.
Pour the batter into the prepared baking pan. Bake for 30 to 45 minutes or until the top of the cake is set and a toothpick inserted into the center comes out clean.
Remove from the oven and transfer to a wire rack to cool completely.