Preheat oven to 350°.
In a large bowl, combine flour, ginger, cinnamon, nutmeg, cloves, baking soda, baking powder, and salt; set aside.
In a separate bowl, cream the butter and sugar together. Then, add the milk, applesauce, molasses, vinegar, and vanilla to that bowl. Pour the dry ingredients into the bowl, then whisk everything together until the batter is smooth.
Grease a 9x13 baking dish, then pour batter into the dish. Alternatively, you can use three 6" round pans if you prefer. Bake cake for 38-42 minutes, or until a toothpick comes out clean. Wait 10 minutes, then carefully invert the cake onto a cooling rack and allow the cake to come to room temperature before icing it.