Preheat the oven to 350°F/180°C. Lightly spray and line with parchment paper a 9x13-inch (23x33-cm) pan. Set aside. Place the oven rack to the center of the oven.
Grate the carrots. Using a small grate size, finely grate the washed and peeled carrots.
Sift the dry ingredients. Into a medium sized bowl, sift the dry ingredients of flour, baking powder, baking soda, cornstarch, salt, cinnamon, and ginger. Set aside.
Mix the wet ingredients. In a large mixing bowl with a hand mixer, or in a stand mixer with the whisk attachment, add the oil, soy milk, applesauce, brown and white sugar, flaxseeds, vanilla, grated carrots, and raisins and pumpkin seeds.
Combine. Slowly add the sifted dry ingredients into the wet ingredients. Mix until the batter is thick and fully combined. Pour into the prepared baking dish.
Bake. Bake for 40 to 45 minutes or until a toothpick inserted into the center pulls out clean. Let the cake cool in the pan for about 15 minutes before removing to a wire cooling rack to finish cooling completely.
Make the frosting. In a large bowl with a hand mixer, or in a stand mixer with the whisk attachment, combine the vegan cream cheese, vegan butter, powdered sugar, and vanilla extract. Whisk on high speed until light and fluffy. Spread over top of the cake and serve. Slice and enjoy!
