Combine 50 grams (approximately 3 1/2 tablespoons) butter with the sugar, vanilla sugar and eggs in a bowl and mix in quark by the spoonful. Beat with a hand mixer briefly but thoroughly.
Stir in the applesauce and semolina, then fold in the mango.
Brush a rectangular baking pan (20 x 30 cm) (approximately 8 x 12 inches) with the remaining butter and pour in the batter. Bake on the middle rack of preheated oven at 180°C (fan 160°C, gas mark 2) (approximately 350°F/convection 325°F) until set, about 40 minutes. If the cake is browning too quickly, cover loosely with aluminum foil during the last 10 minutes.
Allow the cheesecake to cool slightly in the pan. Cut in half lengthwise and then cut each half into 6 (about 5 x 10 cm) (approximately 2 x 4 inch) pieces. Wrap up firmly to transport.