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

Season chicken pieces with 1/2 teaspoon salt and the black pepper. Heat 1 tablespoon olive oil in a large deep skillet over medium-high heat. Add chicken in a single layer and cook 3-4 minutes per side until golden and cooked through (165°F). Transfer to a plate.

In the same skillet, add remaining 1 tablespoon olive oil and reduce heat to medium. Add garlic and sun-dried tomatoes; sauté 1 minute until fragrant, scraping up any browned bits.

Pour in heavy cream and chicken broth, stirring to combine. Bring to a gentle simmer and cook 2-3 minutes until slightly thickened. Stir in remaining 1/2 teaspoon salt.

Add spinach to the skillet a handful at a time, stirring until wilted. Return cooked chicken and any juices to the pan, then add drained penne and Parmesan. Toss well, adding reserved pasta water a splash at a time until the sauce coats the pasta nicely.

Remove from heat. Taste and adjust seasoning. Serve immediately in bowls, garnished with torn basil and extra Parmesan.