Preheat the oven to 350F. Line the bottoms of three 6-inch-round cake pans with parchment paper. Do not grease the sides!
In a bowl, whisk together the egg yolks and 1/2 cup of the sugar until pale. Add the olive oil, vanilla and water and mix until combined.
In the bowl of a stand mixer, whip the egg whites with the cream of tartar on medium speed until light and frothy. Add 1/4 cup of the sugar and continue to beat on high until stiff peaks form.
To the egg yolk mixture, add the flour, baking soda and salt and mix gently to combine and create a paste. Add 1/4 of the egg whites and fold in to lighten the batter. Fold in the remaining egg whites, little by little, until evenly incorporated. Divide evenly among pans.
Bake 15-18 minutes until a cake tester inserted near the center comes out clean. Transfer to wire racks and let cool completely. Once cool, run a knife around the cakes to release, then invert onto wire racks.
While the cakes cool, make the frosting. Melt the white chocolate in a microwave until smooth. Do not overheat- heat little by little, stirring vigorously every instance you take it out of the microwave to avoid heating as much as possible. Set aside and whip the cream immediately.
To the bowl of a stand mixer, add the whipping cream. Beat until soft peaks form. Add the white chocolate slowly and beat on high until well combined and the frosting has some stiffness to it. Fold in the powdered, dried raspberries completely.
Assemble the cake by leveling each cake layer with a serrated knife (if not level already). To the bottom layer, add 1/4 of the frosting. Top with 1/2 of the jam. Repeat with the next layer. To the final layer, use the remaining frosting to cover the cake completely. Sprinkle with remaining raspberry powder, if you desire, for decoration.