FOR THE ICE CREAM DOME: The day before, in medium round bowl that can fit about 3-cup of liquid, lightly brush the inside of the bowl with vegetable oil. Line the inside with a plastic wrap and make sure there is overhang. If needed, use 2 pieces of plastic wrap.
Leave the vanilla ice cream at room temperature until slightly soften, about 15 – 30 minutes. Scoop desired amount into the bottom of the bowl. Smooth the top with a spatula. Transfer to freeze for at least 1 hour.
Place the raspberry sorbet at room temperature until slightly soften, about 15 – 30 minutes. Scoop desired amount to the bowl on top of the vanilla ice cream. Smooth the top with a spatula. Freeze for another 1 hour.
For the chocolate ice cream, leave at room temperature until slightly soften, about 15 – 30 minutes. Scoop desired amount and spread on top of the raspberry sorbet. Do not fill all the way to the top, leaving ½-inch space. Freeze for 1 more hour.
FOR THE CAKE: Preheat the oven to 350˚F (177˚C). In a rimmed quarter sheet pan or 9 x 13 baking pan, lightly grease with vegetable oil. Line with parchment paper (including the sides) and lightly grease with vegetable oil again.
In a large mixing bowl, sift together cake flour, cocoa powder, 1/2 of the sugar, baking powder, and salt. Whisk to combine. Meanwhile, in a small bowl, whisk together oil, water, and egg yolks. Pour into the flour mixture and whisk until just smooth.
In a large mixing bowl with an electric mixer fitted with a whisk attachment, beat the egg whites on medium-low speed until foamy, about 1 minute. Turn on the speed to medium-high and whip for another minute. Slowly add the remaining sugar. Whip until soft peaks form, about 2 minutes. Mix 1/3 of the egg whites to the chocolate mixture to loosen up. Fold in the rest of the whites gently until just combined.
Pour the batter into the prepared baking sheet. Spread evenly with a spatula. Bake in the oven for 10 - 13 minutes, or until cake springs back when pressed lightly in center.
Remove the cake from oven and transfer to a wire rack. Cool for 5 minutes. Invert cake onto the wire rack. Remove the parchment paper carefully and reinvert cake onto a second wire rack. Let cool completely, at least 45 minutes.
Transfer the cake to a cutting board. Cut and trim a round piece of cake to fit on top of the ice cream dome. Place the cake on top of the ice cream and push down gently. Cover with plastic wrap. Freeze for at least 1 hour. Save the cake scraps for yourself.
4 hours before serving, unmold the ice cream cake, unwrap and flip onto a small baking sheet. Return to freezer.
FOR THE MERINGUE: Prepare a double boiler. In a large pot with 1-inch water, bring to a boil and reduce to simmer.
In an electric mixer mixing bowl, add sugar and egg whites. Set over the simmering water. Whisk until mixture is very warm, about 4 minutes. Remove bowl. With an electric mixer fitted with a whisk attachment, beat meringue at high speed until glossy and thick, about 2 – 4 minutes.
ASSEMBLY: Take out the cake. Scoop a good cup of meringue on top of the cake. By moving quickly, spread the meringue evenly over to cover. Make sure the meringue reach the sponge cake and the ice cream is sealed inside, but it doesn’t have to touch the baking sheet. There should be at least ½-inch thick of meringue over the cake. Using the back of a spoon, create peaks and swirls. Return the cake to the freezer and freeze for at least 3 hours.
TO SERVE: If you have a blowtorch, brown the meringue until golden brown. If you don’t have a blowtorch, do it in the oven. Preheat the oven to 500˚F (260˚C). Transfer the cake from freezer directly to oven. Bake until the meringue is deep brown in spots, about 3 – 4 minutes. Slice and serve.