Preparation

Make the cake

• Position a rack in the lower third of the oven and heat the oven to 325°F. Have ready an ungreased, not non-stick 10×4-inch (16-cup) angel food cake pan.
• Separate the eggs, putting the yolks into a small bowl and the whites into a medium bowl.
• Sift the flour into the bowl of a stand mixer or a large mixing bowl. Whisk in the brown sugar, baking powder, cinnamon, ginger, nutmeg, and salt. Add the egg yolks, oil, applesauce, and vanilla. Using the stand mixer fitted with the paddle attachment or a hand-held mixer, beat on medium-low speed until blended. Increase the speed to medium high and beat until lighter in color and thick enough to form a slowly dissolving ribbon of batter when the paddle is lifted, about 3 minutes. Add the carrots and orange zest and beat on medium speed until evenly blended, about 45 seconds.
• Using the stand mixer fitted with a clean bowl and the whisk attachment or a hand-held mixer, beat the egg whites on medium-low speed until foamy, about 1 minute. Increase the speed to medium, and beat until the whites are opaque and form very soft peaks, about 1-1/2 minutes. Slowly add the granulated sugar, and beat until the whites are thick and shiny and form soft peaks, about 1-1/2 minutes.
• Using a rubber spatula, scrape about one-fourth of the whites into the batter and gently fold until blended. Add the remaining whites and gently fold until just blended with no visible streaks of either the whites or batter.
• Immediately scrape the batter into the cake pan. Bake until deep golden brown and springy when touched, about 60 minutes. The top will have cracks around the middle that will look moist inside. Immediately invert the pan onto its feet or by sliding the center tube onto the neck of a bottle, if necessary. Let cool completely. Remove from the pan and place on a flat serving plate.

Ice the cake

• Put the cream cheese and honey in a small bowl. Using a hand-held mixer, beat on low speed until well blended. Increase to medium and continue beating until smooth. Add the heavy cream and stir until well blended. The icing should be very thick but loose enough to fall from a spoon. If it isn’t, add up to 1 Tbs. additional heavy cream, 1 tsp. at a time. Spoon the icing into a heavy-duty zip-top bag. Press and scrape it into one corner and press out any excess air. Seal tightly, snip off a 1/8- to 1/4-inch-wide tip from one corner, and gently squeeze the icing over the top of the cake to form a pattern of thin ribbons. Sprinkle all over with the walnuts.
• The cake can be served immediately or covered and stored at room temperature for up to 3 days.