Preheat oven to 350 degrees F (175 degrees C).
In a medium bowl whisk together All-Purpose Flour (1 1/2 cup), Granulated Sugar (1 cup), Baking Powder (2 teaspoon), Ground Ginger (1 tablespoon), Ground Cinnamon (1 1/2 teaspoon), Ground Allspice (3/4 teaspoon), Ground Nutmeg (3/4 teaspoon), Ground Cloves (1/2 teaspoon) and Salt (1/2 teaspoon).
In a large bowl whisk together Egg (3), Canola Oil (1/2 cup), 2% Reduced Fat Milk (1/2 cup) and Vanilla Extract (1 teaspoon). Add dry ingredients and whisk until just combined. Stir in Parsnip (2 cup).
Line the bottoms of three 8-inch round cake pans with parchment and spray sides with Nonstick Cooking Spray (to taste). Divide batter evenly into each pan and spread out with a spatula (about 13 ounces per pan). Bake on center rack for 17-20 minutes, until a toothpick inserted comes out clean. Remove from oven and allow to cool completely.
To make the simple syrup, combine Granulated Sugar (1/4 cup) and Water (1/4 cup) in a small saucepan over medium heat. Bring to a boil stirring until sugar is dissolved. Once at a boil, allow syrup to boil for 1 minute. Remove from heat and stir in Brandy (1 tablespoon). Allow to cool completely before brushing on the cake.
To make the cream cheese icing beat Unsalted Butter (6 ounce) and Cream Cheese (8 ounce) together until light and fluffy. Add Powdered Confectioners Sugar (2 cup), Ground Cinnamon (3/4 teaspoon), Ground Ginger (1/2 teaspoon), Salt (1 pinch) and Vanilla Extract (1 teaspoon). Beat until just combined.
Remove cake from pans and peel off parchment. Brush each layer with the simple syrup. Arrange one layer on a serving plate and spread with approximately 1/4 of icing. Top with another layer and repeat with icing and top with the remaining cake layer.
Ice the top, reserving a small amount of icing to fill in the layer sides. Run a bench scraper or long straight edge spatula around the outside of the cake to smear and flatten the icing into a "naked cake" look. Dust the top with cinnamon and cut into desired wedges.