Heat the olive oil in a large pot over medium heat. Add sausage and brown it. Remove from pan and set aside.
Add the diced onion and minced garlic, and sauté until the onion is soft and translucent, about 5 minutes. Add the sliced carrots to the pot, and cook for another 5 minutes, stirring occasionally..
Add in the diced yams and sautee for another 5 minutes.
Add sausage back into pan, can white beans and canned tomatoes. Cook, about 5 minutes. I love using beans in soups.
Pour in the chicken or vegetable broth, scraping the bottom of the pot to release any flavorful bits.
Stir in the dried thyme, dried rosemary, salt, and pepper. Bring the soup to a simmer, then reduce the heat to low and let it cook, partially covered, for 20-25 minutes, or until the vegetables are tender.
Taste and adjust the seasoning with more salt and pepper, if needed.
Ladle the soup into bowls garnish with parmesan and enjoy piping hot. You can add fresh herbs if desired.