Preheat the oven to 350°F (175°C). Grease a 9×13-inch baking dish.
Arrange the torn croissant pieces evenly in the prepared baking dish.
Scatter the diced ham over the croissants.
Sprinkle the Swiss and cheddar cheese evenly over the top.
In a large bowl, whisk together the eggs, milk, heavy cream, Dijon mustard, garlic powder, onion powder, salt, pepper, and parsley until smooth.
Pour the egg mixture evenly over the croissants, gently pressing the bread down so it absorbs the custard.
Let the casserole rest for 15 minutes before baking.
Bake for 40 to 45 minutes, or until the center is set and the top is golden brown.
Allow the casserole to cool for 10 minutes before serving.
Garnish with additional chopped parsley if desired.