In a small bowl, combine yeast and sugar. Add just enough warm milk from the measured quantity to form a thick mixture. Rest for 10 minutes until foamy.
In a large bowl, add the yeast mixture, remaining milk, egg, salt, and flour. Mix with a spatula until a shaggy dough forms.
Knead using a stand mixer or hand mixer for 3–5 minutes, or by hand for about 5 minutes, until the dough comes together.
Add the soft butter and continue kneading until the dough is smooth, elastic, and slightly tacky. This will take 5–6 minutes with a mixer or 8–10 minutes by hand.
Transfer the dough to a greased bowl, cover, and let rise in a warm place for about 1½ hours or until doubled in size.
For the mulberry compote, cook mulberries with sugar until thick and reduced. Turn off heat, stir in cornflour, and let cool completely.
Prepare the cream cheese filling by whisking cream cheese, egg, sugar, and vanilla until smooth.
Make the crumble by rubbing melted butter, flour, and brown sugar together until crumbly.
Gently deflate the risen dough. Divide into 8 equal portions. Shape into balls and roll each into a 3–4 inch disc.
Place on lined baking trays, cover loosely, and let rise for 30 minutes.
Press an indentation into the centre of each bun using a floured spoon or glass.
Fill with cream cheese mixture, top with mulberry compote, and generously sprinkle crumble on top and sides.
Bake in a preheated oven at 200°C (392°F) for 15–18 minutes until golden.
Cool on the tray for 10 minutes, then transfer to a wire rack to cool completely.
