Preheat and Toast Bread: Preheat your oven to 350°F (175°C). Spread the sourdough cubes in a single layer on a large baking sheet. Bake for about 10 minutes, until lightly toasted and crisp. Remove from the oven and set aside to cool.
Sauté Aromatics: Place a large, oven safe Dutch oven or pot over medium high heat. Add the 6 tablespoons of butter. Once melted, add the sliced leeks and celery. Cook, stirring occasionally, for about 10 minutes, until softened.
Cook Mushrooms and Herbs: Add the chopped mushrooms, sage, thyme, rosemary, and parsley to the pot. Cook for another 10 minutes, stirring occasionally, until the mushrooms have released their liquid and most of it has evaporated.
Combine Bread and Mixture: Add the toasted sourdough cubes to the pot. Gently toss to coat the bread evenly with the mushroom and herb mixture.
Add Binding Liquid: In a medium bowl, whisk together the eggs, chicken broth, salt, and pepper. Pour the mixture evenly over the bread and mushrooms. Gently toss again to ensure everything is well moistened.
Bake: Place the uncovered pot in the preheated oven. Bake for 25 minutes, until the top is golden brown and crispy, and the stuffing is set.
Garnish and Serve: Carefully remove the pot from the oven. Garnish generously with fresh parsley, a sprinkle of flaky sea salt (if using), and a final drizzle of the 3 tablespoons of melted butter. Serve hot.