Preheat the oven to 350°. Grease a standard 10-inch bundt pan very well with baking spray (the kind with flour in it), then set it aside.
In a medium bowl, stir together the flour, baking powder, cinnamon, ginger, salt, nutmeg, baking soda, and cloves. Set aside the dry ingredients.
In a large mixing bowl, whip together the sugar and butter with an electric mixer or in the body of a stand mixer with the paddle attachment over medium speed. Mix until well combined and smooth for 3 minutes.
Add in vegetable oil and mix to combine.
Next, add in eggs and egg yolks, and mix until just incorporated. Add in vinegar and vanilla and mix to combine.
Add the flour mixture to the wet ingredients and mix until just combined, scraping down the sides of the bowl as needed. Add in the fresh carrots and fold in using a rubber spatula.
Transfer the carrot cake batter to the prepared bundt pan and smooth out.
Place into the preheated oven on the center rack and bake for 45 minutes, or until a toothpick inserted into the center comes out clean or with a few moist crumbs. If any batter is left on the toothpick, it needs to be baked longer.
Once baked, remove from the oven and place onto a wire cooling rack to cool for 10 minutes. Once the cake has cooled for 10 minutes, place a cooling rack on the opening of the bundt pan. Next, flip the cake and cooling rack over simultaneously, allowing the cake to release from the pan.
Let the cake cool completely before frosting.
During the cooling process, make the glaze. Combine cream cheese, powdered sugar, milk, and vanilla in the bowl of a stand mixer fitted with a paddle attachment or in a large bowl with an electric hand mixer.
Mix on low speed until the powder sugar is incorporated, then turn the mixer speed up to medium-high and beat for about 3 minutes.
Once the cake has cooled, place it on a serving plate. Spread the frosting on top and sides of cake with an offset spatula or spoon. Sprinkle chopped pecans on top, then cut into slices and serve.
Notes
This makes a standard-sized bundt cake, but you can easily double it to feed more and make two cakes.
Tons of custom options, see my tips above on that.
Great for a make-ahead dessert since it will keep in the fridge for days.
This freezes well, see my tips above on how to store.
Use all-purpose flour in place of cake flour, see the correct conversion in the FAQ section above.