Preheat oven to 425°F. Butter a 9×13-inch baking dish; set aside.
In a large bowl, whisk together milk, eggs, salt and pepper until smooth.
Cut leftover cornbread into 1-inch cubes and arrange in a single layer in the bottom of prepared baking dish. Sprinkle evenly with green onions, parsley, rosemary, thyme and cheese. Pour milk mixture evenly over and let stand 10 minutes to soak into cornbread.
Bake for 35 to 40 minutes, until golden brown and set. Serve hot.
For an even more decadent version, substitute half and half or heavy cream for some of the milk.