Preheat oven to 200°C.
In a medium bowl, combine both flours and butter.
Using your fingertips, rub the butter through the flours until you have a breadcrumb consistency, then add ¾ of the cheese combination and milk and work into a dough ball with your hands.
When these ingredients are combined, lightly flour your kitchen bench and gently push the dough out into a rectangle, approx 1 cm in depth.
Spread Vegemite evenly over the top of the dough and sprinkle with remaining cheese.
Roll the dough into a long rope shape, rolling it away from you. When you have a rope of dough cut it into eight equal rounds and place them on a lined baking tray.
Brush with milk.
Bake for 20 minutes then remove from oven and cook on wire rack.