Pour the leek mixture over the bread and sprinkle with the herbs. Toss with a wooden spatula, until well coated. Pour the broth evenly over the stuffing and toss to coat. Add the eggs and toss again. If the bread you are using is very dense or dry, you may need to add a little bit more broth. The mixture should be pretty wet.
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 with a piece of foil, for 30 minutes. Uncover the dish and bake for 5 to 10 more minutes to crisp the top a bit. Let rest 10 minutes before serving.