Place the eggs and 1 cup brown sugar in the bowl of an electric mixer and whisk at medium-high speed for 8 minutes, or until thick and doubled in volume. Combine remaining ingredients — carrots, almond flour, coconut, dates, salt, spices, baking powder, oil, and vanilla — in a large bowl, tossing to combine. Fold the carrot mixture into the beaten egg mixture, trying to deflate the eggs as little as possible, and spoon the mixture into your prepared cake pan. Smooth the top of the cake so that it’s level.
Bake for 50 to 60 minutes but please note: A toothpick inserted into the center will come out clean of batter as early as 35 to 40 minutes but it will not be baked enough (i.e. the crumb might be damp and might even seem a little underbaked in the center) unless you take it another 10 to 15 minutes. The cake is forgiving of what you might think is overbaking, even if the sides seem dark.
Remove cake from oven and immediately run a knife around the cake, to loosen anywhere that might be stuck. Let cool for 15 minutes in pan on a rack, then flip it out onto a baking rack, peel off the parchment, and let cake cool right side-up until it’s at room temperature. I usually hurry this along either outside on a cold day or in the fridge.
Make the frosting: [See Note about cream cheese temps in the post] In a stand mixer, food processor, or with a hand-mixer: Beat or blend cream cheese, sugar, sour cream, and and vanilla paste and extract until creamy and light.
To frost and decorate: Spread 2/3 (just eyeball it) of frosting on cooled cake and spread it in a thin, smooth layer. Place the remaining frosting in a bag and snip the corner off. Pipe overlapping squiggles around the cake until you’re out of frosting.
Do ahead: Keep leftover cake in fridge. It keeps (without seeming dry, hooray) for 5 to 6 days.