Prepare a shallow baking tray with baking paper. Preheat oven to 200oC.
Sift flour, baking powder and salt into a bowl. Rub in butter until mixture resembles fine breadcrumbs. Stir in enough milk to make a soft dough. Knead gently on a lightly floured surface. Roll flat to form a 40cm x 25cm rectangle.
Spread vegemite over the dough and sprinkle over 3/4 of the cheese. Roll up the dough along the long side to enclose the cheese. Cut into 14 x 4 cm pieces and place close together, cut side up, on the baking tray.
Sprinkle with remaining cheese and bake in the oven for 15-20 minutes or until cooked and golden.