Line a rimmed baking sheet with parchment paper. Place cubed sourdough bread onto the baking sheet. Drizzle with olive oil, salt, and pepper. Bake for 20-30 minutes until crunchy and lightly browned. Let cool.
Increase oven temperature to 350°F.
In a large skillet, melt 4 tablespoons butter over medium heat. Add onions and celery. Cook until softened, about 8 minutes. Add sausage to the pan and cook until the meat is no longer pink, breaking up the meat with a spatula. Add the garlic, parsley, sage, rosemary, thyme, poultry seasoning, salt, and pepper. Stir to combine. Transfer to a large bowl to cool.
In a medium bowl, whisk together chicken broth and eggs. Pour broth over the cooked onion mixture and stir to combine. Add the bread cubes. Gently stir to coat each piece of bread, allowing the bread to soak up the liquid.
Pour mixture into a buttered 9x13-inch dish. Bake on the middle rack for 45 minutes or until golden on top. Garnish with chopped herbs.