Place the cream cheese and butter in a large bowl; beat with electric mixer until smooth and creamy. Beat 60g icing sugar into the butter mixture. Slowly beat in the flour; mix well. Cover bowl and refrigerate at least 3 hours or overnight.
Preheat oven to 190 C / Gas 5.
On a well floured board, roll out chilled dough to 3mm thick. Use a pizza cutter to cut dough into 6.25cm squares. Spoon approximately 2 teaspoons of the compote in the centre of each square; do not overfill. Fold opposite corners of each square into the middle to encase dough, pinching dough together in centre. Filling should peek out a little at each end. Transfer pastries to an ungreased baking tray.
Bake the kolache in the preheated oven until set but not brown, about 12 minutes. Remove to racks to cool. Dust cooled kolache with remaining icing sugar.
If you can't get your hands on apricot compote, use a high fruit apricot jam instead.