Grease a 9x13-inch baking dish with butter or cooking spray.
Spread the bread cubes evenly in the bottom of the dish. Top with diced ham, onion, bell pepper, and both cheeses.
In a large bowl, whisk together eggs, milk, heavy cream, Dijon mustard, garlic powder, salt, and pepper until well combined.
Pour the egg mixture evenly over the bread and ham mixture, making sure to cover everything. Press down gently with a spatula to help the bread soak up the liquid.
Cover with plastic wrap and refrigerate for at least 2 hours or overnight (overnight is best!).
When ready to bake, preheat your oven to 350°F and remove the casserole from the refrigerator to take the chill off while the oven heats (about 15-20 minutes).
Drizzle the melted butter over the top of the casserole.
Bake uncovered for 45-50 minutes until the top is golden brown and the center is set (a knife inserted in the center should come out clean).
Let it rest for 5-10 minutes before cutting. Garnish with fresh chives and serve warm!