Combine yeast, buttermilk, sugar and ¼ cup warm water in the bowl of an electric mixer and stand for 10 minutes or until foamy. Add flour, butter, eggs and a pinch of salt and mix using dough hook attachment. Turn onto a floured surface and knead until smooth, place in a lightly oiled bowl, turn to coat, cover with plastic wrap and stand for 1 hour or until doubled in size.
Turn dough onto a lightly floured surface and roll to 3mm thick. Using a 7.5cm-round cutter dipped in flour, cut out rounds, re-roll dough and repeat. Divide milk chocolate among half the rounds, placing in centre, brush edges with milk and top with remaining rounds. Using a 6.5cm-round cutter dipped in flour, trim rounds, pressing to seal. Place 2cm apart on a lightly floured tray and stand for 30 minutes or until doubled in size.
Heat oil in a large deep saucepan or deep-fryer to 160C. Deep-fry doughnuts, in batches, turning occasionally for 2-3 minutes, or until puffed and golden. Roll in cinnamon sugar and serve immediately.