Preheat oven 350º F. Coat two 8-inch cake pans with butter or shortening and lightly dust with flour to prevent cake from sticking while baking. Alternately, coat well with baking spray.
Mix together butter, coconut oil, granulated sugar, and brown sugar in a large bowl with an electric mixer until well combined. Mix in vanilla extract until well incorporated. Add eggs one at a time, beating well after each addition before adding the next. Add egg yolk making sure well combined.
Whisk together flour, baking powder, baking soda, cinnamon, ginger and salt in a medium bowl.
Add half of the flour mixture to the butter and sugar mixture and beat until well incorporated. Add buttermilk, beating until just combined before stirring in remaining flour mixture.
Fold in carrots, 1 cup of pecans and divide the batter between the two prepared cake pans.
Bake until cakes spring back when gently touched in the center and the edges begin to turn loose from the sides of the pan, about 30 - 40 minutes. Remove from the oven and allow to cool in the pans on a wire rack for about 5 minutes. Turn out of pans and allow to cool completely on a wire rack.
Frost cake with cream cheese frosting.
1 - I use White Lily all-purpose flour, which is made of 100% soft winter wheat. If White Lily flour is not available, you may want to use cake flour instead. 2 - Additional mix-ins may be included or used in place of the 1 cup of pecans. I would recommend coconut, raisins, walnuts, or even pineapple. The total amount of mix-ins should not exceed 1 cup. 3 - I only used half of the cream cheese frosting recipe for the cake photographed and did not spread frosting on the sides of the cake.