Preheat your oven to 350°F.
Grease the 9x13 inch baking dish thoroughly.
Cut croissants into 1-inch pieces.
Layer croissant pieces in the prepared dish.
Sprinkle diced ham evenly over croissants.
Add both cheeses on top.
Whisk eggs in large mixing bowl.
Add milk, cream, mustard, salt, and pepper.
Pour egg mixture over croissant layers.
Cover dish with foil tightly.
Bake for 30 minutes covered.
Remove foil and bake 15 minutes more.
Let rest 10 minutes before serving.
Garnish with fresh chives before serving.