Use paper towels to pat chicken thighs super dry, then season both sides with salt & pepper (I use 1/4 tsp salt & 1/2 tsp pepper). Heat 1 tbsp oil from the sun-dried tomatoes and 1 tbsp butter in a large pot over medium-high heat. Once the butter starts foaming, add chicken in a single layer, smooth side down. Cook for about 3 minutes, or until lightly golden and it releases easily from the pan. Flip and cook another 3 minutes, then transfer to a bowl or plate. (Doesn't need to be cooked through, it will finish cooking later!)
Reduce heat to medium. Add remaining 1 tbsp butter, then the onions & carrots. Sauté for 7–9 minutes, taking the time to get the veggies nice & tender. Add garlic and cook, stirring constantly, for 1 minute. Sprinkle flour over everything and cook for another minute, stirring constantly.
Gradually add 1 cup of broth, whisking constantly until smooth. Add the remaining broth slowly, whisking and scraping the bottom of the pot. Add Italian seasoning.
Bring broth to a boil, then add pasta. Cook for 4 minutes, stirring often so it doesn’t stick. Meanwhile, cut chicken into small bite-sized pieces. Add chicken (plus any juices left behind in bowl/plate) and cook for about 4-6 more minutes, or until pasta is al dente and chicken reaches 165°F.
Reduce heat to low. Stir in cream & sun-dried tomatoes. Add Parmesan gradually, 1/4 cup at a time, stirring until melted before adding more. Stir in spinach & vinegar and cook just until spinach wilts. Taste and add salt as needed. Add more broth for a thinner soup, if desired.
Serve hot with hearty buttered bread on the side.
Notes
Note 1: A good chicken broth makes a big difference in flavor. I recommend Swanson®. If you’re worried about saltiness, use low-sodium broth, then add a little extra salt at the end if needed.Note 2: The secret to this soup is good Parm! Use refrigerated, finely grated Parmesan (the sandy-textured kind). Skip the shelf-stable kind for the best flavor & smoothest melt.Storage: Store leftovers in an airtight container for 3 days. The pasta will keep soaking up the broth, so use a wire skimmer ladle to separate the solids from the broth and store them separately.