Preheat oven to 350 degrees and grease and flour a 9-inch springform pan (other options include a bundt pan, 9 x 13 inch pan, or two 9-inch cake pan (for 9-inch cake pans, those with 3-inch tall sides will allow cake to rise higher than 2-inch tall sides)
Combine all dry ingredients (except sugar) in small bowl and set aside
In a large bowl, combine eggs, oil, sugar and vanilla and mix on medium speed for about 3 or 4 minutes until well combined, scraping down sides of the bowl to ensure no lumps remain
Add dry ingredients to wet ingredients and mix only until combined while scraping down sides of the bowl intermittently.
Stir in carrots and nuts.
Pour batter into prepared pan and bake for 70 to 90 minutes if using 9-inch springform pan; for 60 to 80 minutes if using a bundt cake pan. (if you are using another type of cake pan, please see NOTE 1).
Begin testing cake at 65 minutes by inserting cake tester in center. Cake is finished when the tester comes out dry (there is no batter on the tester)
Cool cake completely before frosting.
For the Frosting
In the meantime (while cake is baking), combine all frosting ingredients in mixing bowl and beat on medium speed until creamy
Butter must be room temperature or your frosting will be lumpy.
If you'd like to fill the cake as well as frost it, prepare 2 batches of the frosting recipe (ie, double the amount of each ingredient)
To Decorate Cake
After cake has completely cooled, fill with frosting if desired, frost top and sides, and decorate as desired. We used a star tip to add some swirls on top edges after frosting.
To Store and Serve
This cake is best served at room temperature, and it will not dry out as long as it's kept in a cake stand with a lid or a container large enough to enclose it.
If it has been sliced, place plastic wrap on the expose sides to create a seal that locks out any air from getting to the cake.
If refrigerating the leftover cake If refrigerated, it can harden a bit but it will soften nicely once it comes to room temperature. If you are questioning whether the cream cheese needs refrigerating, you can leave it out overnight provided your kitchen is not too hot. If in doubt, refrigerate it.
To Freeze: You can totally freeze this cake by the slice so that you have some at your disposal whenever the craving strikes! Just wrap securely in freezer-safe plastic wrap and place in an airtight, freezer-safe container or plastic bag. Allow it to thaw to room temperature before enjoying!
NOTE 1. If you don't have white whole wheat flour, use all purpose flour instead for a total amount of 2 ¾ per cake that you make. NOTE 2: If you would like to include a layer of filling as shown in the photo, double the amount of frosting (cake shown in picture used two batches of the frosting recipe).NOTE 3: For frosting, use powdered erythritol in place of powdered sugar to cut sugar grams by nearly 50% per serving (without filling). Using two 9 by 3-inch cake pans; bake for approximately 30 to 35 minutes (start testing at 25 minutes); if using a 9 x 13 cake pan, bake for about 35 to 40 minutes (start testing at 30 minutes). Nutrition information estimates calories without filling (only frosting).