Spread a thin layer of mustard over each croissant half, then make 8 sandwiches using the ham and gruyère as the filling.
Whisk together the eggs, milk and cream, then season really well. Butter a 35cm-diameter ovenproof dish and arrange the croissants at the bottom. Pour over the eggy mixture and leave for 15 minutes, turning now and again to help it all soak in.
Heat the oven to 180C/fan 160C/gas 4. Bake the croissants for 20-25 minutes or until the egg mixture is just set. Scatter with chives before serving.