In a large pot over medium-high heat, warm 1 tablespoon oil. Add the sausage, break into chunks, spread them out, and cook undisturbed for about 2-3 minutes or until deeply browned. Then stir it up and continue to cook until cooked through, breaking into bite-sized pieces and reducing the heat as needed. Transfer to a bowl.
Add the remaining 1 tablespoon oil to the pot over medium heat. Stir in the bell pepper, celery, and ½ teaspoon salt and cook for about 5 minutes or until softened. Stir in the fennel, turmeric, pepper, and garlic for 30 seconds, then add the water, sweet potatoes, mushrooms, beans, soy sauce and remaining 1 teaspoon salt.
Bring to a boil, then simmer rapidly over medium-low heat for about 15 minutes or until the potatoes are cooked through, stirring every 5 minutes to ensure the potatoes are getting cooked evenly.
Turn off the heat and stir in the kale.
Serve the soup topped with the sausage, an egg yolk, fresh herbs, and black pepper. Stir the yolk into the hot soup for a velvety broth!