3/4 cup (1 1/2 sticks) unsalted butter plus more for baking dish
1 pound good-quality day-old white bread, torn into 1-inch pieces (about 10 cups)
2 1/2 cups chopped yellow onions
1 1/2 cups 1/4-inch slices celery
1/2 cup chopped flat-leaf parsley
2 tablespoons chopped fresh sage
1 tablespoon chopped fresh rosemary
1 tablespoon chopped fresh thyme
2 teaspoons kosher salt
1 teaspoon freshly ground black pepper
2 1/2 cups low-sodium chicken broth, divided
2 large eggs
Preheat oven to 250°. Butter a 13x9x2-inch baking dish and set aside. Scatter bread in a single layer on a rimmed baking sheet. Bake, stirring occasionally, until dried out, about 1 hour. Let cool; transfer to a very large bowl.
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.
Preheat oven to 350°. Whisk 1 1/4 cups broth and eggs in a small bowl. Add to bread mixture; fold gently until thoroughly combined. Transfer to prepared dish, cover with foil, and bake until an instant-read thermometer inserted into the center of dressing registers 160°, about 40 minutes.
Continue to bake dressing, uncovered, until set and top is browned and crisp, 40–45 minutes longer.