Preheat oven to 350℉. Lightly grease a 9 x 13 inch baking dish.
Dry the bread: Spread the cubed sourdough bread on a baking sheet and bake for 10 - 15 minutes, until slightly crisp and dry. (You can skip this step if using day-old bread.)
Saute the vegetables: In a large skillet, melt 1/2 cup butter over medium heat. Add onion, celery, and garlic; cook 5 -7 minutes until softened.
Add seasonings: Stir in salt, pepper, sage, parsley, rosemary, and thyme. Cook 1 - 2 minutes, just until fragrant.
Combine: In a large bowl, toss the bread cubes with the sauteed vegetable. Pour in 1 1/2 cups broth and mix gently. Add beaten eggs and stir until evenly coated, adding more broth as needed. The mixture should be moist but not soggy. Add more broth if needed.
Bake: Transfer to your prepared dish, drizzle with 1 tablespoon of melted butter, and bake uncovered for 40 - 45 minutes, until golden brown on top.
Serve: Sprinkle with extra parsley and serve warm with your holiday feast.