2) Meanwhile, in the bowl of an electric stand mixer, whisk the egg whites, the remaining 500g of sugar, and the cream of tartar to medium peaks. Once the syrup has reached 115 degrees C, start to drizzle the hot sugar syrup into the meringue while the beaters are running. Continue until all of the syrup is used and then continue to whip the meringue until it cools to room temperature.
3) Slowly add in the softened butter; the mixture will tend to curdle. Continue to mix until all of the butter has been incorporated; the buttercream will eventually come together, becoming a smooth mixture in the end. Make sure to scrape down the bowl from time to time while mixing. Divide the mixture into 2 large sheet pans, cover securely, and refrigerate until ready to use.
Make the cake:
4) Lightly spray a size 400 hotel pan or large sheet pan with non-stick cooking spray and then line with parchment paper; set aside. Preheat the oven to 200 degrees C.
5) Sieve the cake flour at least twice and set aside. Cream the eggs and sugar in a mixing bowl, beating until a pale yellow color. Gently fold in the cake flour. When this stage is almost completed, fold in the melted butter. Spread the genoise batter onto the prepared sheet pan. Bake for 10 to 12 minutes or until a toothpick inserted into the center of the cake comes out clean. Cool cake in the pan for 10 to 15 minutes, and then remove to a rack to cool completely before frosting.
6) While cake cools, make a simple syrup by combining 220g sugar and 225ml water in a heavy saucepan over high heat; bring to a boil and then remove from the heat and let cool.
7) Cut the cakes into 4 equal pieces so that they will fit perfectly on top of each other. Brush the bottom cake layer with simple syrup and then brush it with framboise. Brush a thin layer of raspberry marmalade on top and then apply a layer of the buttercream-Italian meringue. Repeat 2 more times. For the fourth and final cake layer, brush it with simple syrup and then framboise, but do not apply the marmalade. Frost the top and the sides of the cake, smoothing it out until perfect.