Preheat the oven to 350°F (180°C).
Spray a 9 x 13-inch (33 x 22.9 cm) baking dish with non-stick cooking spray.
Slice open and stuff each croissant with a slice of ham then arrange them in one layer in the baking dish.
In a large bowl, whisk the eggs together with the milk, mustard, chives, and season with salt and pepper.
Pour the mixture over the croissants. Gently press down on the croissants allowing them to absorb the egg mixture.
Sprinkle the cheddar and parmesan cheeses evenly on top.
Cover the dish with foil and bake for 25 minutes. Remove the foil, then continue baking for another 10 minutes or until the croissants are golden on top. Serve warm.