In a large dutch oven, heat the olive oil over medium heat. When the oil is heated, add the potatoes onions, carrots and celery stalks. Cook for about 5 minutes or until onions are transparent. Add the garlic and cook for one additional minute. If you are using caraway, add it at this time.
Add the vegetable broth and deglaze the pan. Cover and simmer on low for 30 minutes.
While the soup is simmering, sear the sausaged in a small skillet over medium heat until golden brown. Set aside.
When the soup is finished, turn off the heat and stir in the salt, pepper and yellow mustard and parsley.
Serve with sausages on top.