Preheat the oven to 350 degrees.
Grease a 9x13 inch baking dish with butter to prevent the sourdough stuffing from sticking.
Cut the sourdough bread into cubes and place the cubes on a baking sheet. Bake for 10-15 minutes, until the bread is "stale" and hard.
While the bread toasts, take the sausage out of the casing and add it to a saute pan with the butter. Cook for 5 minutes until the sausage is no longer pink.
Add the chopped celery, onions, and sliced mushrooms to the pan. Cook for another 5 minutes until the vegetables are softened.
Add the chopped herbs to the pan and mix everything together.
Place the bread cubes into a large bowl. Add the sausage and mushroom mixture to the bread cubes and toss to combine.
In a liquid measuring cup, measure out 3 cups of broth. Crack the two eggs into the broth and whisk well to combine the broth and eggs.
Add the broth mixture to the bread mixture and toss all the ingredients to combine. Season with salt and pepper to your liking.
Cover the baking dish with aluminum foil and bake for 45 minutes. After 45 minutes, take the aluminum foil off of the baking dish and bake for 15 minutes longer until the top is browned to your liking. Serve immediately.