Preheat the oven to 350°F and grease an 8x11 or 9x13-inch baking dish.
Tear the bread into 1-inch pieces and place in a very large bowl.
Melt the 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. Pour the leek mixture over the bread and sprinkle with the sage, parsley, rosemary, and thyme. Use your hands to toss until coated. Pour 1½ cups of the broth evenly over the stuffing and toss to coat. Add the eggs and toss again. The bread should feel pretty wet. If it’s still a bit dry, mix in the remaining ½ cup of broth. The amount you use will depend on how dense and dry your bread was.
Transfer the mixture to the baking dish. If making ahead, stop here, cover the dish with foil, and store in the refrigerator until ready to bake.
When ready to bake, drizzle the olive oil on top and bake, covered, for 30 minutes. If the stuffing is still pretty wet, uncover the dish and bake for 5 to 10 more minutes to crisp the top a bit.