Preheat the oven to 350 degrees. Grease 3 6" inch round cake pans with non stick spray and line the bottoms with parchment paper rounds. Set aside.
In a medium bowl, whisk together the all purpose flour, cinnamon, nutmeg, ginger, allspice, baking powder, baking soda and salt. Then set aside.
2 ½ cups (313 g) all-purpose flour, spooned and leveled, 1 tablespoon cinnamon, ½ teaspoon ground nutmeg, ½ teaspoon ground ginger, ½ teaspoon ground allspice, 1 ½ teaspoon baking powder, ¼ teaspoon baking soda, ½ teaspoon salt
In a large bowl, cream together the butter, granulated sugar and light brown sugar with an electric mixer on high speed until fluffy, about 3-4 minutes. (If using a stand mixer, use the paddle attachment.)
10 tablespoon (140 g) unsalted butter, softened, 1 cup (200 g) granulated white sugar, ½ cup (110 g) packed, light brown sugar
Then add in the eggs and vanilla and mix on medium then medium-high speed until smooth, pale in color and slightly fluffy, about 2-3 minutes. Scrape the sides of the bowl with a rubber spatula as needed.
3 eggs, at room temperature, 1 teaspoon vanilla bean paste or extract
Alternate adding the dry ingredients and the buttermilk to the butter mixture a little at a time, until each has been added completely. Mix on low then medium speed just until the batter is combined and smooth, scraping the sides of the bowl as necessary.
¾ cup (178 ml) buttermilk, at room temperature
Add in the shredded carrots and mix on low speed just until dispersed through the batter.
2 cups (220 g) finely shredded carrots, at room temperature
Evenly distribute the cake batter between the prepared cake pans. Bake the cakes for 36-41 minutes, or until a toothpick comes out clean from the centers. Let the cakes cool in the pans for 5 minutes, then transfer to a wire rack to completely cool.