Make the cake:

1. Preheat oven to 350°F.
2. Grease two 8-inch round cake pans with butter. Line the bottom of each pan with a circle of parchment paper and then butter the parchment paper.
3. In a medium bowl, whisk together the flour, baking powder, baking soda, cinnamon, nutmeg, salt, cloves, and ginger.
4. In a large bowl, whisk together the sugar, oil, eggs, and vanilla until smooth. Stir in carrots and pecans, then gently fold in the flour mixture just until combined.
5. Divide batter between the prepared pans.
6. Bake until center of cakes feel firm to the touch, about 25-28 minutes, rotating halfway through baking time.
7. Let cakes cool completely before frosting.

For the frosting:

1. While the cakes are cooling, prepare the frosting.
2. In the bowl of a stand mixer fitted with the paddle attachment, beat the butter on low speed, slowly adding the confectioners' sugar until smooth. Add vanilla and a pinch of salt and continue mixing. Increase speed to medium and add cream cheese gradually, mixing until smooth.

Assemble and frost the cake:

1. Using a serrated knife, carefully slice the rounded top off from each cake layer so that both layers have a flat top.
2. Arrange one layer on a cake plate and spread the top with frosting. Top with remaining layer of cake. Continue frosting the top and sides of the cake with the remaining icing, and decorate with spiced pecans, if desired.
3. Refrigerate 1 hour, or until ready to serve.