Preheat the oven to 350 F. Grease and line an 8x8 pan with parchment paper.
Mix the dry ingredients: In a large bowl, combine the flour, baking soda, salt, cinnamon, and pumpkin pie spice.
Mix the wet ingredients: In a separate bowl, whisk together the neutral oil, white sugar, brown sugar, eggs, vanilla extract, and pumpkin purée. Carefully fold the dry ingredients into the wet ingredients in 2 parts. Fold until just combined, being careful not to overmix.
Grate and fold the grated carrots into the batter. Pour the batter into the lined pan and bake for 20-25 minutes. A toothpick inserted into the cake should come out clean.
Allow the cake to cool down completely before cutting it into four squares to make four cake boxes, or cut the slices to your preference.