Preheat the oven to 325°F. Line an 8x8" glass baking pan with unbleached parchment paper.
In a large mixing bowl, combine all of the dry ingredients: flour, sugar, baking powder, baking soda, salt, cinnamon, ginger, nutmeg, & cloves. Stir everything together.
Add the oil, eggs, applesauce, and molasses. Stir until a smooth batter forms. It may seem a little thicker than traditional cake batter, but that is okay.
Spread the batter into the 8x8" glass baking dish. It may not spread out completely smoothly, but that is okay too. The batter will loosen up when it bakes and smooth out the top.
Bake for 40-45 minutes. A toothpick inserted into the center should come out clean, the center of the cake should be set, and the cake should bounce back when pressed lightly.
Allow the cake to cool completely on a wire cooling rack before frosting or slicing the cake. Store leftovers in an airtight container for 2-3 days.