Cut or tear the bread into 1-inch cubes and spread evenly on 2 baking sheets. Toast in the oven until completely dry and beginning to crisp and brown (about 20 minutes). Take out to cool.
Melt the ghee in a large cast iron skillet over medium to high heat. Add the mushrooms, water chestnuts and a few pinches of salt. Sauté, stirring occasionally, until golden brown (about 6 to 8 minutes).
Add celery, garlic, onion, sage and thyme. Cook until onions, mushrooms and water chestnuts are sauteed.
Take off the heat, add the broth and sourdough bread cubes. Season with salt and pepper. Mix gently until all the liquid is absorbed.
Cover the skillet with foil and cook in the oven at 180°C for 15 minutes. Remove foil and cook for another 20 minutes, or until top is golden. Take out of the oven and let cool for a few minutes.
Sprinkle with sesame seeds and chopped parsley before serving.