Bring a large pot of salted water to a boil. Cook the pasta according to package directions until al dente, typically 8-10 minutes. Before draining, reserve about 1/2 cup of the starchy pasta water, then drain the pasta and set aside.

While the pasta cooks, season both sides of the chicken breasts generously with salt and pepper. Heat olive oil in a large 12-inch skillet over medium-high heat until shimmering. Add the chicken and cook for 5-7 minutes per side until golden brown and internal temperature reaches 165°F. Remove from skillet and set aside to rest.

In the same skillet with the chicken drippings, add the minced garlic and sauté for about 1 minute until fragrant but not browned. Stir in the chopped sun-dried tomatoes and cook for another minute.

Pour in the heavy cream and chicken broth, stirring to combine and scrape up any browned bits from the bottom of the pan. Bring the mixture to a gentle simmer, then gradually whisk in the grated Parmesan cheese. Keep stirring until the cheese melts completely and the sauce thickens to coat the back of a spoon, about 3-4 minutes.

Slice the rested chicken into strips and return it to the skillet along with the fresh spinach. Add the cooked pasta and Italian seasoning, tossing everything together in the creamy sauce. Cook for 2-3 minutes until the spinach wilts and everything is heated through. If the sauce seems too thick, add a splash of the reserved pasta water to reach your desired consistency.