Preheat the oven to 350°F and grease a baking dish with butter.
Slice each croissant in half horizontally. Layer 2 to 3 slices of turkey ham and 1 to 2 slices of cheddar cheese inside each croissant, then close them back up. Feel free to add more or less meat and cheese depending on your preference.
Cut each filled croissant into four equal sections and arrange them snugly in the prepared baking dish.
In a bowl, whisk together the eggs, half and half, mustard, salt, and pepper until smooth.
Pour the egg mixture evenly over the croissants, making sure they soak up the custard. Let it sit for 5 minutes.
Dot the top with butter and cover with foil.
Bake covered for 20-25 minutes. Uncover and cook for 10 more minutes or until golden brown and set.
Serve warm and enjoy!