Bring a large pot of generously salted water to a boil and cook the pasta until just before al dente. Before draining, reserve 1 cup of the pasta cooking water. In a large bowl, toss the chicken with 2 tablespoons of oil from the jar of roasted tomatoes (or 1 to 2 tablespoons extra-virgin olive oil), Italian seasoning, paprika, ¾ teaspoon salt, and ½ teaspoon black pepper. Heat a large oven-safe skillet over medium heat, add the chicken, and sauté until fully cooked, about 8 minutes. Remove the chicken and set aside in a bowl. Add the shallots to the skillet, adding a little more oil if necessary, and cook until softened, about 3 minutes. Stir in the garlic and crushed red pepper flakes, cooking until fragrant, about 1 minute. Mix in the roasted tomatoes (or sun-dried tomatoes) and fresh spinach, cooking until the spinach wilts, about 2 to 3 minutes. Season with the remaining ½ teaspoon salt. Stir in the pesto and heavy cream. Add the cooked pasta and ½ cup of the reserved pasta water, stirring constantly until the sauce thickens and coats the pasta. Add more pasta water as needed until the sauce reaches a creamy, thick consistency (usually the full cup). Stir in ⅓ cup of the grated Parmigiano-Reggiano cheese and the cooked chicken. Preheat the oven broiler to HIGH. Sprinkle the torn mozzarella and the remaining Parmigiano-Reggiano cheese evenly over the pasta. Place the skillet under the broiler and broil until the mozzarella melts and starts to brown, about 3 to 4 minutes. Garnish with chopped fresh basil and serve immediately.
