Preheat your oven to 220°C/200°C fan-forced. Line a baking tray with baking paper. Sift the flour into a bowl. Using fingertips, rub butter into flour until mixture resembles breadcrumbs. Make a well in the centre. Add the milk. Using a flat-bladed knife, stir until mixture forms a soft dough, adding more milk if necessary. Turn out onto a lightly floured surface. Knead gently until smooth (make sure you don't over-knead).
Roll dough out to a 30cm x 20cm rectangle. Spread the Vegemite over the dough, leaving a 1cm strip along 1 long side. Sprinkle with the cheese over the Vegemite. Roll up firmly. Transfer to prepared tray, seam-side down.
Using scissors, cut into top of dough at 3cm intervals without cutting all the way through. Pull slices to the left and right. Brush with milk. Bake for 20 to 25 minutes or until golden.