In a large pot, or Dutch oven, heat the olive oil over medium heat. Add the onions to the pan and cook until beginning to soften, about 3-4 minutes. Add in the garlic and carrots and cook, stirring frequently, just until fragrant, about 1-2 minutes.
Add chicken stock and red wine vinegar and bring to a simmer over medium heat.
In a separate pot, cook the pasta according to the directions on the package. Set aside.
Once the broth is simmering, squeeze the sausages out of their casings by pinching and twisting at 1/2 half intervals, creating little balls of meat and squeezing them into the simmering broth. Let the balls cook in the broth for approximately 5 minutes, or until firm and fully cooked. Add salt and pepper to taste.
Once the sausage balls are fully cooked, add in spinach and cook for a minute or two, until it wilts.
Add in pasta, or you can add the pasta to the bowls separately so that the pasta wont absorb all the broth if you have leftovers. The latter is the method I favor.