For the brittle, melt 50 g of sugar in a pan without fat and let it caramelise. Turn the hazelnuts in it. Leave to cool on an oiled flat plate. Melt the fat in a pan and let it cool down a little. Mix flour and baking powder in a bowl. Add 150 g sugar and vanillin sugar.
Add the fat and knead into crumbles with the dough hooks of the hand mixer. Press about 2/3 of the mixture into a greased springform pan (26 cm Ø). Chop the brittle roughly on a board. Mix 2/3 of the brittle into the remaining crumbles and set aside. Wash, peel and quarter the apples and cut out the core. Cut the apple quarters into slices. Mix with remaining sugar, except for a teaspoon, and lemon juice and zest. Spread on the crumb base and sprinkle with the brittle crumbles. Bake in the preheated oven (electric: 200°C/ gas: level 3) for 40-45 minutes. If necessary, cover with parchment paper at the end of the baking time. Let the cake cool down in the tin on a cake rack. Whip cream and remaining sugar until stiff.
Mix with remaining sugar, except for a teaspoon, and lemon juice and zest. Spread on the crumb base and sprinkle with the brittle crumbles. Bake in the preheated oven (electric: 200°C/ gas: level 3) for 40-45 minutes. If necessary, cover with parchment paper at the end of the baking time. Let the cake cool down in the tin on a cake rack. Whip cream and remaining sugar until stiff. Pour into a piping bag with star-shaped spout and decorate the cake with cream tuffs. Sprinkle the remaining brittle on the tuffs