Preheat the oven to 400 degrees. Line a baking sheet with tinfoil. Place the halved tomatoes and chicken breasts on the baking sheet, drizzle with the 3 Tablespoons of olive oil and generously salt and pepper everything. Bake for 20-30 minutes until the chicken is cooked through and the tomatoes are caramelized, with browned edges.
While those cook, heat the 1 Tablespoon of olive oil in a large skillet over medium heat and cook the onions until very soft, about 10 minutes.
Bring a pot of water to a boil and add the pasta and let it cook until al dente while you make the sauce.
Add the garlic to the onion pan, cook for about 30 seconds, then add the cream, chicken broth, Parmesan, and italian seasoning. Cook over medium-low heat, stirring frequently, until it is smooth and thickened.
Slice up the chicken breasts. Add the chicken, the roasted tomatoes, and the spinach to the sauce and let cook 1-2 minutes until the spinach is slightly wilted. Salt and pepper to taste.
Serve the sauce over the pasta and top with the basil, if desired.