Cut breadstick into 3cm thick slices on the diagonal, but not all the way through.
Spread each cut side of bread alternately with butter then Vegemite and place in a piece of cheese. Continue until each split has Vegemite and cheese in each. Wrap in foil and bake at 180°C fan-forced for 10 minutes.
Unwrap the top of the foil, to expose the top of the breadstick, and return to the oven for a further 5 minutes.