Melt the butter in a saucepan over low heat. Add the grated cheese, milk or whisky, mustard and a seasoning of salt and pepper. Stir until the cheese has melted and the mixture is smooth. Do not overcook at this stage or cheese will become oily. Draw off the heat and allow to cool slightly. Meanwhile, separate the egg and whisk the egg white until stiff peaks form. Stir the egg yolk into the cheese mixture, then fold in the egg white.
Have the hot toast slices ready and place on a grill-pan rack. Spoon the rarebit mixture on to each slice and spread evenly. Place under a hot grill and the rarebit mixture will puff up and brown beautifully.