The night before preparing this recipe, tear or cut your bread into 1-inch pieces and leave uncovered on the counter overnight to allow it to dry out.
The day of, preheat the oven to 350°F and grease a 9x13-inch baking dish. Melt ½ cup of butter in a large skillet over medium heat. Add the leeks, celery, garlic, salt, and pepper, and sauté for 5 minutes, turning the heat to low halfway through. Add the wine to the pan and allow it to simmer for about 3-5 minutes, scraping up any browned bits on the bottom of the pan as it simmers. Take the leek mixture off the heat and set aside.
Add crusty bread pieces to a large bowl. Pour the leek mixture over the bread and sprinkle with the sage, parsley, and thyme. Use your hands to toss until coated. Pour 2 cups of the broth evenly over the stuffing and toss to coat. Add the eggs and toss again. The bread should feel fairly wet. If it still feels dry, slowly add in the remaining broth, ¼ cup at a time.
Transfer the mixture to the baking dish. If making ahead to cook later, stop here, cover the dish with foil, and store in the refrigerator or set aside until ready to bake.
When ready to bake, drizzle 4 tablespoons of melted butter evenly over the top and bake, covered, for 30 minutes. Uncover and bake for 10 more minutes, until the top is lightly browned and slightly crispy.