In a large Dutch oven, heat 1 tbsp olive oil and butter on medium-high heat. Season the chicken thighs with salt, pepper, and garlic powder. Place the chicken thighs, smooth side down, into the Dutch oven and brown for about 5 minutes. Flip and cook the other side for about 5 minutes more, or until the chicken is just about cooked through. Remove them from the Dutch oven and place them on a plate, tented with foil.
Reduce the heat to medium. Add the remaining olive oil, then the tomatoes and shallots. Cook until the skins start blistering on the tomatoes, about 3 minutes, stirring often. Stir in the zucchini and garlic; cook for 1 minute more. Season with salt to taste.
Pour in the white wine and reduce to about 3/4 cup, about 3 minutes. Stir in the tomato paste and Italian seasoning.
Pour in the chicken broth, cover, and allow it to come to a rapid simmer over high heat. Once it starts to simmer, stir in the pasta and basil. Reduce the heat to medium. Cook until the pasta is al dente and the liquid has mostly reduced, but still has enough for the sauce, about 15-17 minutes.
During the last 5 minutes of cooking, add the chicken thighs on top of the pasta and the juices that accumulated with it, then cover and allow them to cook until the internal temperature of the thighs reaches 170F.
Uncover and reduce the heat to medium-low. Pour in the heavy cream, then stir in the parmesan. Let it gently simmer for about 5 minutes until slightly thickened. Once the sauce coats the back of a spoon, it's ready.
Serve immediately, and garnish with fresh parsley.