Use the finest grater (but not a zester) to grate the carrots - if you don't have a fine grater, use a knife to further mince the grated carrot. Set aside.

In a large bowl, whip together the egg yolks and the honey for a minute. Stir in the grated carrots, rum, and vanilla. Stir in almond flour.

In a medium bowl whip egg whites until soft peaks form, then gradually add sugar. Stir a third of the egg whites into the carrot mixture to loosen the batter. Gently fold the remaining egg whites in, taking care not to deflate the batter.

Divide the batter between 2-8" parchment lined pans (don't grease the sides), and bake at 375°F for 10 minutes. Lower to 350°F and continue baking another 30 minutes or until toothpick comes out clean. Let cool 15 minutes before removing from pan.

For the frosting, beat together the butter and cream cheese until smooth. Slowly add the icing sugar, beating until smooth. Add the vanilla and spread over the cooled cake.