Tear the croissant dough along the perforations. For each croissant, unroll and lay 2 slices of ham on top of the dough, trying to keep the ham within the dough's outline, then lay 1 cheese slice over the top (this needs to be thin to be able to roll). Lightly spread with the mustard.
Roll up the croissants, gently curl into a crescent shape and place on the baking sheets. Brush with beaten egg, then sprinkle with the Parmesan.
Bake in a preheated oven, 200°C (400°F), Gas Mark 6, for 10–15 minutes until well risen and golden. Serve warm.