Carrot-Spice Cake with Coconut-Pecan Filling

Begin with cake layers: Place carrots in a large saucepan; cover with cold water. Bring to a boil, then reduce heat to medium-low and boil until tender, about 20 minutes. Drain any remaining water. Transfer carrots to a food processor or blender; add 1 tablespoon of the butter. Puree until completely smooth. Measure out 1 cup puree. Let cool. (To cool faster, spread puree in a pie plate and place in refrigerator.)

Meanwhile, preheat oven to 350°. Butter and flour 3 9-inch cake pans; set aside. In a medium bowl, whisk together flour, baking powder, ginger, cinnamon and the 1 teaspoon salt; set aside.

In a stand mixer fitted with the paddle attachment beat remaining butter (15 tablespoons) on medium-high speed until fluffy, about 2 minutes, scraping bowl about halfway through. Add all but 2 tablespoons sugar; fluff another 2 minutes, scraping once. Beat in the 4 egg yolks, one at a time. Stop and scrape down sides of the bowl. On low speed, add flour mixture and carrot puree in alternating scoops until the batter glows a smooth pale orange, scraping down sides of bowl as needed. Transfer cake batter to a large mixing bowl, set aside.

Clean the mixer bowl and use the whisk attachment to beat egg whites foamy; pour in remaining 2 tablespoons sugar, beat to sturdy peaks, scraping down bowl once or twice. With a rubber spatula, fold whites gently and thoroughly into batter.

Divide batter among the 3 prepared pans. Bake until a toothpick poked in the center comes out clean, about 25 minutes. Let cool in pans, 10 minutes. Turn each layer out on a rack and let cool completely.

Meanwhile, prepare Coconut-Pecan Fluff Filling. In a dry skillet over medium heat, toast pecans, shaking pan regularly, until nuts darken and give off a lovely scent, about 5 minutes. Watch closely to make sure the nuts don't burn. Let cool.

In a large saucepan, melt 1/2 cup unsalted butter over medium heat. Whisk in dark brown sugar, coconut milk, 4 egg yolks and the 1/2 teaspoon kosher salt. Cook, whisking, until thickened, about 10 minutes. Strain through fine-mesh sieve into a clean stand-mixer bowl; press a piece of plastic wrap against the surface and chill in refrigerator. (To speed chilling, you can place the bowl in an ice bath.) When cool, beat until fluffy in a stand-mixer fitted with the paddle attachment, about 4 minutes. Fold in toasted pecans.

Begin assembling the cake. Set one layer on a platter. Spread evenly with half the filling. Stack with a second cake layer and spread on the remaining fluff. Top with the third layer. Cover cake with plastic wrap (to avoid it drying out), and set aside while preparing frosting.

For frosting: In the clean bowl of a stand-mixer fitted with the paddle attachment, beat cream cheese, 1/2 cup butter and 1 teaspoon vanilla on medium speed until light and fluffy. Gradually beat in 4 cups powdered sugar to reach spreading consistency, adding more sugar to thicken if needed. Spread a thin layer over the top and sides of the cake to seal in crumbs. Place in refrigerator for 15 minutes. Finish frosting the cake, swirling for effect.