For the cake: Position rack in center of oven for LA (lower position at 8,500’). Preheat the oven to 320°F. Line bottom and sides of a deep 9” cake pan (I use a springform pan) with parchment paper.
In a large bowl, whisk together the eggs, sugar and vanilla until well blended and slightly foamy. Add the almond flour, coconut, salt and spices and mix well. Mix in the melted butter thoroughly. Finally, mix in the carrots and walnuts. Transfer the batter to the prepared pan, making top even.
Bake until a crust forms and cake is firm to the touch, 1 hour to 1 hour 15 minutes (mine took 1 hour 15 minutes at 2,000’ and 1 hour 10 minutes at 8,500’, check at 1 hour). Cool completely on a rack. Cake is best if allowed to stand for a day before serving.
For the frosting: Soften the cream cheese and butter by letting stand 2 hours at room temperature, or place in a microwave safe bowl and warm in the microwave at low setting just until soft enough to mix with a spoon, about 10 seconds. Using a wooden spoon, mix together until smooth. Add the powdered sugar and vanilla and beat with spoon until smooth.
Remove the parchment from the cake and transfer the cake to a serving platter. Slide sheets of waxed paper under edges of the cake to keep platter clean while decorating. First make a thin layer of frosting on the top to catch any crumbs by placing small dollops of frosting over the top of the cake and smoothing to cover. Then spread frosting over sides of the cake. Now add more frosting to the top and smooth. Remove the waxed paper. Chill at least 1 hour to set the frosting. (Keeps chilled up to 5 days. Place 4 toothpicks into top of frosted cake, then gently cover with plastic wrap.)
Garnish cake with flowers or walnuts. (Decorated cake can be refrigerated for 1 day or even up to 2 days if flowers aren’t too delicate.) Let cake stand at room temperature at least 1 hour before serving.