Preheat the oven to 375°F and grease a 9x13-inch or similar baking dish.

Spread the cubed cornbread on a large baking sheet and bake for 10 minutes, or until lightly crisp and golden brown.

Heat the olive oil in a large skillet over medium heat. Add the onion, celery, salt, and pepper and cook for 8 to 10 minutes, or until soft. Stir in the garlic.

Place the toasted cornbread in a large bowl. Add the onion mixture, the sage, rosemary, and parsley. Stir to combine, then add 2 cups of the vegetable broth and the eggs and mix until the cornbread is evenly moistened. If it feels dry, add more vegetable broth as needed to moisten it. I typically use up to another 1/2 cup.

Transfer to the prepared baking dish and drizzle with the melted butter. Cover and bake for 25 minutes, then uncover and bake for another 15 to 25 minutes, or until the top is lightly crisp and golden. Garnish with fresh parsley and serve.