Grease 2 8-inch cake pans and line the bottoms with parchment paper.
In a medium mixing bowl, whisk together flour, baking powder, baking soda, salt, cinnamon, nutmeg, and allspice. Set aside.
In another mixing bowl, combine the shredded carrots and the walnuts. Set aside.
In another bowl, combine granulated and brown sugars. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment (or in a large mixing bowl using a hand mixer), beat eggs and oil at medium speed for 2 minutes.
Reduce speed to low and slowly add sugar. Once all sugar is added, scrape bowl, then beat for 1 more minute.
Add vanilla, lemon zest, and sour cream or greek yogurt. Beat for one minute, then scrape the bowl and mix for another 30 seconds.
Add carrots and walnuts, beating on low until well-distributed throughout the batter, about 1 minute. Scrape bowl.
Slowly add half of the flour mixture. Mix on low for 1-2 minutes, then scrape the bowl. Slowly add the rest of the dry ingredients and mix on low for 1-2 minutes.
Divide batter evenly between the prepared pans. Bake for 35-40 minutes, or until a toothpick inserted into the center of the cake comes out clean.
Cool in the pans for 10 minutes, then turn them out onto a cooling rack and allow to cool completely before frosting.
Honey Cinnamon Cream Cheese Frosting
In the bowl of a stand mixer fitted with the paddle attachment (or in a mixing bowl, using a hand mixer), beat the butter and cream cheese for 2-3 minutes on medium-high speed or until light and fluffy.
Add vanilla, honey, and cinnamon. Mix well.
Add powdered sugar a little at a time, mixing until combined. Scrape bowl.
Beat on medium-high speed until fluffy, another 2 minutes or so.
To frost the cake, place one layer on your serving plate. Scoop 1/3 of the frosting on top, and spread evenly.
Place the second cake layer on top. Scoop half of the remaining frosting on top, and spread evenly.
Use the remaining frosting to cover the sides of the cake.
Decorate the top of the cake with more walnuts, then slice and serve! Store leftover cake in an airtight container in the refrigerator.
Notes
*Feel free to sub raisins for part or all of the walnuts, and if you like pineapple in your carrot cake, swap the sour cream for 1/4-1/2 c crushed pineapple (drained well).