Preheat the oven to 180º C and butter a large 35cm skillet pan or ovenproof dish.
Spread a thin layer of Dijon mustard over each croissant half and place a slice of ham in each one. Divide up the grated Comté between the 8 croissants and then arrange them across the bottom of the dish.
In a large jug or bowl, whisk together the eggs, whole milk, ¾ of the cream cheese (save the rest for later) and double cream and then season well with freshly ground black pepper.
Pour over the croissants and leave for 10 minutes to allow some of the liquid to get soaked up.
Bake the croissants in the oven for 25-30 minutes until golden brown and bubbling.
Dollop over the remaining cream cheese and chopped chives and serve immediately.