Bring a large pot of salted water to a boil for the pasta. Cook the pasta according to package directions until al dente, reserving about 1/2 cup of the pasta water before draining. This starchy water helps loosen the sauce later.
While the pasta cooks, season the chicken with a pinch of salt and pepper. In a large skillet, heat the olive oil over medium-high heat. Sear the chicken pieces until golden brown on both sides and cooked through, about 4-5 minutes per side depending on thickness. Remove the chicken from the skillet and set aside.
In the same skillet, add a touch more oil if needed and sauté the minced garlic for about 30 seconds until fragrant. Stir in the sun-dried tomatoes and continue to cook for another minute to release their sweetness.
Pour in the chicken broth and bring to a gentle simmer. Add the heavy cream and bring back to a simmer. Whisk in the Parmesan cheese until the sauce is smooth and slightly thickened.
Return the chicken to the skillet along with any juices that have collected. Add the Italian seasoning and a pinch of salt and pepper. If the sauce seems too thick, add a little of the reserved pasta water until you reach a creamy, coat-the-spoon consistency.
Stir in the spinach until just wilted, then fold in the cooked pasta. If using mozzarella pearls, scatter them in and let them melt gently. Taste and adjust seasoning as needed.
Remove from heat and serve immediately. A light grating of extra Parmesan on top adds a nice finish. Garnish with fresh chopped parsley or a squeeze of lemon for brightness, if you like.