Preheat oven to 350 degrees F. Grease or line an 8x4 loaf pan, set aside.
In a mixing bowl combine the flour, cinnamon, nutmeg, allspice, salt, baking soda, and baking powder, mix to combine.
In a large mixing bowl combine the oil and sugar, whisk well to combine. Add in the eggs and vanilla. Slowly add in the dry ingredients and mix to combine.
Gently fold in the grated carrots. Pour the mixture into the prepared loaf pan and bake 55-60 minutes until the cake is firm and a toothpick inserted comes out clean. Allow the cake to cool completely before frosting.
For the Cream Cheese Frosting:
In a hand or stand mixer fitted with a paddle attachment, cream the cream cheese until fluffy, add in the powdered sugar, milk, and vanilla extract. Mix until light and fluffy.