Preheat oven to 175C (fan forced) and line 2 trays with baking paper.
Place two pastry sheets on a clean work surface. Spread with vegemite and top with half of the cheese. Roll up to enclose filling – brushing the edge with a little of the beaten egg to seal.
Place the other two pasty sheets on a clean work surface. Spread with the tomato paste, and top with ham and the remaining cheese. Roll up to enclose filling – brushing the edge with a little of the beaten egg to seal.
Slice each roll into 8 pieces. Place the pieces, cut side up, on the lined baking trays. Brush the tops with a little beaten egg at this stage if you’d like the scrolls to be even more golden brown).
Bake for 15 to 18 minutes, or until puffed up and golden brown. Allow to cool on the tray for 5 minutes, then move to a wire rack.