In a large bowl, combine quark, oil, milk, sugar, vanilla sugar, and salt and mix well.
In another bowl, whisk together flour and baking powder. Sieve half of the flour mixture into the quark mixture and stir to combine. Knead the remaining flour mixture into the dough by hand until fully incorporated.
On a floured surface, roll the dough to an even thickness. Cut out rounds approximately 10 cm in diameter.
Spread 1 teaspoon of applesauce on one half of each dough round. Brush the edge of each round with milk. Fold each round in half and press the edges together firmly with a fork to seal.
Place the turnovers on a baking sheet greased with fat.
Preheat the oven to 200 °C (392 °F). Bake the turnovers for 15 minutes until golden.
While the turnovers bake, sift the powdered sugar into a bowl and whisk with the hot water until smooth.
Immediately after removing the turnovers from the oven, brush them with the frosting. Allow the frosting to set before serving.