Dice the onion, and mince the garlic. In a large pot over medium heat, add the olive oil and the diced onion. Cook until the onion begins to soften.
Directly into the pot, squeeze the sausage meat from the casings. Break up the meat with a wooden spoon. Cook until the meat is no longer pink. Add the minced garlic and cook until fragrant.
Add the can of diced tomatoes, continuing to cook on medium, while scraping any browned bits from the bottom of the pot.
Peel and dice the carrots.
Add all of the remaining ingredients except the tortellini to the pot. The chicken stock, can of tomato paste, carrots, Italian seasoning and balsamic vinegar.
Cover and reduce the heat to low. Simmer on low until the carrots are soft, approximately 30 minutes.
When the carrots are soft, taste the soup and add salt and pepper to taste. Bring the soup to a rapid boil. Add the tortellini.
Cover the soup once more and simmer on medium low until the tortellini is cooked, approximately 15 minutes. Taste again and add more salt and pepper if desired.