Preheat the oven to 200ºC.
Unroll the puff pastry (working away from yourself) on a lightly floured work surface. Spread Dijon mustard on the pastry but leave a 1 cm edge at the top end. Lay slices of ham onto the pastry covering it all (except for the edges). Sprinkle over the grated cheeses and then top with chives. Roll the pastry up from the bottom and work towards the open end. Brush the open edge with egg wash and continue rolling to close up; lightly press to stick the pastry log together.
Use a sharp serrated knife to slice the log into 1 cm thick pinwheels. Place the pinwheels flat onto a non-stick or baking paper-lined tray. Brush the tops and sides with egg, then bake for 20-25 minutes until golden. Allow to cool slightly and serve.