Peel the onions, cut in half lengthways and thinly slice them with the grain - from root end to tip. This is important for achieving silky caramelised onions.
Place the olive oil, onions, and a good pinch of salt in a medium, heavy based saucepan. Stir together then cover with a lid and place this over a medium/high heat to cook for 3 minutes, to sweat and begin to release their juices and drop.
Stir, then replace the lid, turn down to a medium heat and cook for another 3 minutes before removing the lid, stirring, and cooking over a low heat uncovered for 25 minutes, stiring often, to really begin to caramelise the onions. During this time, make sure you stir through any bits that caramelise and stick to the pan. Once caramelised, remove the onions and set aside to cool.
For the dough, combine the flour, a good pinch of salt and the yoghurt and using a spoon, mix to combine. Tip this out onto a well-floured bench and knead the dough for 2-3 minutes. The dough should be soft and springy. Let this rest for 5-10 minutes, covered in a bowl.
On a floured bench, roll the dough into a rough rectangle 1cm thick and gently spread with the Vegemite, onions and scatter ¾ of the cheese.
Working lengthways, from short ends, fold 1/3 then the other 1/3 from the other side over that to enclose (like a business letter). Roll this back out to 1cm thick then cut into 9 strips. Twist each strip, coil up, tuck in the end underneath, then turn over and place onto the baking tray. Brush with beaten egg and sprinkle with the remaining cheese.
Bake for 15-20 minutes and allow to rest for 2-3 minutes before serving. So good served straight from the oven while warm.