Peel and finely grate the carrot. Mix 100 g butter, 75 g sugar, vanilla sugar and salt with the whisk of the hand mixer for 4-5 minutes until creamy. Stir in the eggs one after the other. Mix flour, 50 g starch and baking powder and stir in briefly. Finally stir in the carrot
Put the dough into a greased, flour-dusted rectangular tart tin (19 x 27 cm) and smooth it down. Bake in a preheated oven (electric cooker: 175 °C/ convection oven: 150 °C/ gas: see manufacturer) for approx. 25 minutes (test with sticks)
Wash apples and grate them dry. Quarter apples, remove core and cut apple quarters into small cubes. Caramelise 75 g sugar with 2 tbsp. water in a pot, add apples, deglaze with lemon juice and simmer for about 3 minutes. Mix 10 g starch with 2 tbsp. water, add to the apples and simmer for about 1 minute, stirring continuously. Let the compote cool down
Take the cake out of the oven and let it cool down on a cake rack. Carefully spread lukewarm compote on the tart base and chill for about 30 minutes. Whip 200 g butter and 75 g icing sugar with the whisk of the hand mixer until creamy white. Stir cream cheese until smooth, add some butter cream and then stir in the remaining butter cream
Spread the cream on the tart and make waves with a cake comb. Chill the tarte for about 15 minutes. Remove the tarte from the tin. Mix 1 tablespoon icing sugar with cinnamon and dust the tarte with it shortly before serving
waiting time approx. 1 1/4 hours