WHAT YOU NEED

For the cake

1 scant cup [210 g] large egg whites (from 6 or 7 large eggs), at room temperature
1 cup [240 g] whole milk, at room temperature
¼ cup [60 g] canola oil
2 tablespoons sour cream, at room temperature
1 teaspoon pure vanilla extract
3 cups [426 g] all-purpose flour
1 cup [200 g] granulated sugar
1 cup [200 g] light brown sugar
4 teaspoons baking powder
2 teaspoons ground cinnamon
1 teaspoon salt
Pinch cloves
12 tablespoons [1½ sticks or 170 g] unsalted butter, at room temperature, cut into 1 in [2.5 cm] pieces
4 cups [400 g] finely grated carrots

For the burnt honey buttercream

1 cup plus 2 tablespoons [280 g] large eggs whites (from 7 or 8 large eggs), at room temperature
¼ teaspoon cream of tartar
1½ cups [300 g] granulated sugar
½ cup [170 g] honey
¼ teaspoon salt
¼ cup [60 g] water
3 cups [6 sticks or 678 g] unsalted butter, at room temperature, cut into 1 in [2.5 cm] pieces
1 teaspoon pure vanilla extract

For the cake

Adjust an oven rack to the middle position and preheat the oven to 350ºF [180ºC]. Grease three 20 by 5 cm circular cake pans and line the bottoms with parchment paper.

In a medium bowl or liquid measuring cup, whisk together the egg whites, milk, oil, sour cream, and vanilla.

In the bowl of a stand mixer fitted with a paddle, whisk together the flour, granulated and brown sugars, baking powder, cinnamon, salt, and cloves by hand until combined. With the mixer running on low speed, add the butter one piece at a time, beating until the mixture resembles coarse sand. With the mixer still running on low speed, slowly add a little more than half of the wet ingredients. Increase the speed to medium and beat until the ingredients are incorporated, about 30 seconds. With the mixer running on low speed, add the rest of the wet ingredients, mixing until just combined. Increase the speed to medium and beat for 20 seconds (the batter may still look a little bumpy). Scrape down the sides and bottom of the bowl, add the grated carrots, and use a spatula to mix the batter until the carrots are incorporated.

Pour the batter into the prepared pans and smooth the tops. Tap the pans gently on the counter a few times to get rid of any bubbles. Bake for 30 to 36 minutes, rotating the pans halfway through, until the cakes are golden brown and a wooden skewer or toothpick inserted into the center comes out with a faint bit of crumbs. Transfer the pans to a wire rack and let cool for 30 minutes. Turn the cakes out onto the rack, remove the parchment paper, and let cool completely.

For the buttercream

In the bowl of a stand mixer fitted with a whisk, beat the egg whites and cream of tartar on medium speed until they are almost able to hold soft peaks, 5 to 7 minutes. Lower the speed to low and add ½ cup [100 g] of the granulated sugar in a slow, steady stream.

Beat on medium speed until the whites are stiff and glossy, 1 to 2 minutes. Let the whites sit in the bowl while you make the syrup.

Place the remaining 1 cup [200 g] of granulated sugar, the honey, and salt in a medium saucepan.

Pour the water over the top and gently stir just enough to wet the sugar, being careful not to mix too much so the sugar doesn’t splash up the sides of the pan. Heat over medium heat, giving the pan a little shake every once in a while, to mix the honey and sugar as they melt. When the sugar has melted and the liquid looks clear (no sugar granulates are noticeable), increase the heat to medium-high and let the liquid bubble and boil until it turns a deep golden brown, 3 to 4 minutes. Remove the pan from the heat.

With the mixer running on low speed, very carefully pour about 2 tablespoons of the hot honey caramel into the egg whites, trying not to hit the sides of the bowl, and mixing until combined (pouring the hot mixture into a liquid measuring cup with a pourable spout works best here). Pour 2 tablespoons more caramel into the egg whites and continue mixing (this will help temper the eggs so they won’t cook). With the mixer running on low speed, pour the rest of the caramel into the whites in a slow, steady stream, still trying not to hit the sides of the bowl. Beat until the mixture is completely combined.

Increase the speed to medium-high and whisk until the bowl cools to room temperature. Lower the speed to low and add the butter one piece at a time, beating well after each addition. Increase the speed to medium and beat until the buttercream is completely smooth, 2 to 3 minutes. Add the vanilla and beat on medium speed for 1 to 2 minutes.

To assemble

Place one layer of the cake on a turntable or serving plate. With an offset spatula, spread the top evenly with 1½ cups [450 g] of the buttercream. Place the second layer on top, and frost with another 1 cup [300 g] of filling. Place the third layer on top and frost the cake, topping with the candied pecans, if desired, and serve. Store the cake, covered, in the refrigerator for up to 1 day.