Make the Cake: Preheat your oven to 325°F (160°C). Coat a 9-inch round (or 8-inch square) cake pan with nonstick spray and line the bottom with parchment paper. Set side.
Place the eggs and 1 cup brown sugar in the bowl of an electric mixer and beat on medium-high speed for 8 minutes or until thickened and doubled in volume. Combine remaining ingredients — carrots, almond flour, coconut, dates, salt, spices, baking powder, oil and vanilla — in a large bowl. Stir the carrot mixture into the beaten egg mixture, trying to remove as little of the egg as possible, and pour the mixture into your prepared cake pan. Smooth out the top of the cake so that it is level.
Bake for 50 to 60 minutes but please note: a toothpick inserted in the center will come out clean with the batter in 35 to 40 minutes but it will not be baked enough (i.e. the crumb may be moist and feel slightly underbaked in the center) Unless you take it another 10 to 15 minutes. The cake is forgiving of what you might think is over-baking, even if the sides look dark.
Remove the cake from the oven and immediately run a knife around the sides of the cake to loosen anything that may be stuck. Let cool in the pan on a rack for 15 minutes, then invert it onto a baking rack, peel off the parchment, and let the cake cool right-side up until it is at room temperature. I usually make it early on a cold day or outside in the fridge.
Make Frosting: [See Note about cream cheese temps in the post] With a stand mixer, food processor, or a hand-mixer: Beat or blend the cream cheese, sugar, sour cream, and vanilla paste and extract until creamy and light.
To Frost and Decorate: Spread 2/3 (just the eyeballs) frosting over the cooled cake and spread it out in a thin, smooth layer. Place remaining frosting in a bag and snip off the corner. Pipe overlapping squiggles around cake until you run out of frosting.
Proceed: Keep the remaining cake in the fridge. It stays on for 5 to 6 days (without drying, hooray).