Preheat your oven to 350°F (175°C). Grease and flour two 8-inch round cake pans, then set aside.
In a medium bowl, whisk together the flour, baking soda, baking powder, salt, cinnamon, nutmeg, and ginger.
In a large bowl, beat the eggs, oil, brown sugar, granulated sugar, and vanilla extract until well combined. Gradually add the dry ingredients to the wet mixture, stirring until just combined.
Gently fold in the grated carrots. The mixture will be thick but that’s what makes the cake so moist.
Divide the batter evenly between your two prepared pans. Bake for 30 minutes or until a toothpick inserted in the center comes out clean. Let the cakes cool in the pans for 10 minutes, then transfer them to a wire rack to cool completely.
Beat the softened cream cheese and butter together until smooth. Add the powdered sugar, vanilla, and a pinch of salt, and continue to beat until the frosting is creamy and spreadable. When you are happy with the consistency, fold in the toasted pecans.
Once the cakes are cool, spread a thick layer of frosting between the two layers, then frost the top and sides. For an extra touch, sprinkle some chopped and toasted pecans on top or add a light dusting of cinnamon.