Bring a large pot of salted water to a boil. Cook penne according to package directions until al dente. Reserve 1/2 cup pasta water, then drain.

While pasta cooks, season chicken pieces with Italian seasoning, salt, and pepper. Heat 1 tablespoon olive oil in a large deep skillet over medium-high heat. Add chicken and cook until golden brown and cooked through to an internal temperature of 165°F (74°C), about 6-7 minutes, turning once. Transfer to a plate and set aside.

In the same skillet, reduce heat to medium. Add remaining 1 tablespoon olive oil if needed. Sauté garlic and sun-dried tomatoes for 1 minute until fragrant.

Pour in heavy cream and chicken broth, scraping up any browned bits from the bottom. Bring to a gentle simmer, then reduce heat to medium-low. Stir in Parmesan cheese and let melt, creating a smooth sauce. Season with a pinch of salt and pepper.

Add the drained pasta and cooked chicken back to the skillet. Toss well to coat. Fold in spinach a handful at a time until just wilted. If sauce is too thick, add reserved pasta water a tablespoon at a time until silky. Adjust seasoning to taste.

Divide among bowls, finish with torn basil, extra Parmesan, and a crack of black pepper. Serve immediately.