Melt the butter in a large skillet over medium-low heat. Cook the diced onions and celery until softened, about 10 minutes. Remove from heat and set aside.
In a large mixing bowl, combine the bread cubes, broth, eggs, cooked onions and celery, fresh herbs and salt. Be sure that all bread cubes are coated and moist.
Transfer the mixture to a 9x9 baking dish. Cover with foil.
Bake 35 minutes, remove the foil and bake 20 more minutes. Serve warm.