Place racks in the upper and lower thirds of the oven; preheat to 300 degrees . Divide the bread between 2 rimmed baking sheets. Bake, stirring bread and switching sheets halfway through baking, until bread is toasted, about 20 minutes. Let cool; transfer to a large bowl. Increase the oven temperature to 375 degrees .
In a skillet, melt the butter over medium-high heat. Add the onions, celery, 1 1/2 tsp. salt and 1 tsp. pepper. Cook, stirring, until the vegetables are soft, about 8 minutes.
In a large bowl, whisk together the broth and the eggs. Pour over the bread. Add the vegetables and herbs; toss to combine.
Transfer the stuffing to a greased shallow 3-qt. baking dish. Bake until the top is browned, about 45 minutes.