Instructions

for the cake

Adjust oven rack to middle position and heat oven to 350 degrees. Grease and flour 8-inch round cake pan. Combine milk, egg whites, and vanilla in 2-cup liquid measuring cup.
Using stand mixer fitted with paddle, mix flour, sugar, baking powder, and salt on low speed until combined, about 30 seconds. Add butter and continue to mix until mixture resembles moist crumbs, with no powdery streaks remaining, about 1 minute. Add half of milk mixture, increase speed to medium, and beat until smooth, about 1½ minutes, scraping down bowl as needed. With mixer running, add remaining milk mixture and beat until fully incorporated, about 30 seconds.
Pour batter into prepared pan and spread into even layer with rubber spatula. Bake until toothpick inserted in center comes out clean, 21 to 25 minutes, rotating pan halfway through baking.
Let cake cool in pan for 5 minutes, then loosen from sides of pan with butter knife. Invert onto large plate, then reinvert onto wire rack. Let cool completely, about 1½ hours.

for the candied orange peel

Meanwhile, using vegetable peeler, remove orange peel in wide strips, avoiding pith. Cut strips lengthwise into thin strips. Place peel in small saucepan and cover with water. Bring to boil over medium-high heat, then strain peel. Return peel to saucepan, cover with fresh water, and repeat.
In now-empty saucepan, bring sugar and ½ cup water to boil over medium-low heat, stirring frequently to dissolve. Add peel and cook until just starting to turn translucent, about 5 minutes. Let peel cool completely in syrup. (Peel can be refrigerated in syrup for up to 2 weeks.)
FOR THE LADYFINGERS: Process marmalade and water in food processor until no large pieces of rind remain, about 30 seconds. Transfer to small saucepan and bring to boil over medium heat. Off heat, whisk in gelatin until dissolved. Let cool slightly, about 15 minutes. Dip each ladyfinger quickly into marmalade mixture, flipping once to coat both sides, then place on wire rack set in rimmed baking sheet.

to assemble

Grease 9-inch springform pan and line bottom with parchment paper. Line sides of pan with 3-inch-wide strip of parchment, then grease parchment. Center cake round in bottom of prepared pan. Line sides of pan with coated ladyfingers, flat sides facing in, gently wedging ladyfingers between cake and pan. Brush 3 tablespoons remaining marmalade mixture (some may be left over) evenly over top of cake. Scoop sherbet into bowl and mash with wooden spoon until softened. Spread in even layer over cake. Cover with plastic wrap; freeze until very firm, at least 2 hours. Scoop ice cream into bowl and mash with wooden spoon until softened. Spread in even layer over sherbet. Cover with plastic; freeze until very firm, at least 2 hours.
To serve, remove sides of pan. Using large metal spatula, transfer cake from pan bottom to plate or pedestal, then gently peel off parchment from sides. Arrange candied peel in center of cake. Serve.