Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper.

In a large mixing bowl, combine the flour, baking powder, and salt. Mix well.

Add the cold, cubed butter to the flour mixture. Use a pastry cutter or your fingers to blend until the mixture resembles coarse crumbs.

Pour in the milk and stir until just combined. Do not overmix.

Turn the dough out onto a lightly floured surface and knead gently for about 1 minute until it comes together.

Roll the dough into a rectangle about 1/2 inch thick.

Spread the Vegemite evenly over the dough, leaving a small border around the edges.

Sprinkle the shredded cheddar cheese evenly over the Vegemite.

Starting from one long side, carefully roll the dough into a tight log.

Slice the log into 1-inch thick pieces and place them cut-side up on the prepared baking sheet.

Brush the tops of the scrolls with the beaten egg.

Bake for 15-20 minutes or until golden brown and cooked through.

Allow to cool slightly before serving.