Preheat oven to 220C/200C fan-forced.

In a bowl, using your fingers rub butter into sifted self-raising flour until mixture resembles breadcrumbs. Make a well in centre. Add 3/4 cup milk. Stir with a butter knife until mixture forms a soft dough, adding extra milk if necessary. Turn onto a lightly floured surface and knead gently until smooth (don't over-knead).

Roll out dough to form a 20cm x 30cm rectangle. Spread Vegemite over dough, leaving a 1cm strip along 1 long side. Sprinkle over 3/4 cup reduced-fat tasty cheese. Roll up firmly from long side. Trim ends. Cut into 8 x 2.5cm thick slices. Place 3cm apart onto 2 baking paper-lined baking trays. Brush with extra milk. Sprinkle with 1/4 cup grated cheese.

Bake for 20 minutes or until golden. Cool and store in an airtight container for up to 2 days.