The night before, spread bread out on a baking sheet. Leave out overnight. (If you forget, you can also dry bread out in the oven that morning- 250 for 1 hour)
Preheat oven to 350°. Butter or spray a 13x9 baking dish and set aside.
Meanwhile, melt 3/4 cup butter in a large skillet over medium-high heat; add onions and celery. Stir often until just beginning to brown, about 10 minutes. Add to bowl with bread; stir in herbs, salt, and pepper. Drizzle in 1 1/4 cups broth and toss gently. Let cool.
Whisk 1 1/4 cups broth and eggs together. Add to bread mixture; fold together gently until combined. Transfer to prepared dish, cover with foil, and bake 40 minutes.
Uncover and bake until top is browned and crisp, 40-45 minutes longer.