Preheat the oven to 190 degrees Celsius/ 370 degrees Fahrenheit. Line a baking tray (approximately 30x40 cm/ 12x15 inches) with baking paper. Set aside.
Beat the egg whites until stiff. Slowly start adding the sugar and beat until the egg whites are stiff and glossy. Incorporate the vanilla extract. Set aside.
Beat the soft butter and sugar until pale and creamy. Add the egg yolks and add them to the batter.
Mix the flour and the baking powder. Mix into the butter mixture alternatively with the milk.
Assemble: Evenly spread the mixture onto the prepared baking tray. Spread the meringue on top of the batter. Sprinkle the meringue with the slivered almonds.
Bake the cake base for 20 minutes. Remove from the oven, transfer the cake together with its baking paper on a wire rack and let cool completely. It will not take that long.
Cut the cake: When the cake is cool, divide it in the middle crosswise, so that you have two equal halves. Run a long knife underneath the cake base to more easily release the baking paper. Place one half on a serving platter.
Whip cream: Pour the heavy cream into a mixing bowl and beat until the cream has the desired consistency. Use cream stabilizer or substitute if desired (see note).
Drain the mandarin oranges well and pat them dry with kitchen paper. Fold them into the whipped cream. Spread the mixture onto the cake on the platter.
Cover with the second cake half and press gently. Keep refrigerated until ready to serve.
If you live in Germany, use 2 packets of Sahnesteif (cream stabilizer) (Amazon affiliate link) to stabilize the whipped cream. However, the cream stabilizer is not always necessary; you will have to decide yourself if the whipped cream is stable enough or not. The cream stabilizer can be replaced with a mixture of icing sugar and cornstarch in a 1:1 ratio. In this case, you will mix 3 teaspoons icing sugar with 3 teaspoons of cornstarch. To use it, beat the cream shortly. Then, slowly start adding the stabilizer or substitute and mix until the cream has achieved the desired consistency.