Bring a pot of salted water to a boil and cook the penne according to package instructions until al dente; drain and set aside.
Heat 1 tablespoon olive oil and 1 teaspoon sun-dried tomato oil in a large skillet over medium-high heat.
Season the bite-size chicken pieces with 1/2 teaspoon salt, 1/4 teaspoon black pepper, and 1 teaspoon Italian seasoning, then add to the skillet and cook until no longer pink and cooked through, about 5–7 minutes; transfer the chicken to a plate.
Add a little more oil to the pan if needed, then sauté 2 teaspoons minced garlic and 1/4 cup chopped sun-dried tomatoes for 3–4 minutes until fragrant.
In a bowl or large measuring cup, whisk together 2 cups half-and-half (or whole milk) and 1 tablespoon cornstarch until smooth.
Pour the milk mixture into the skillet with the garlic and tomatoes, add 1/4 cup of the shredded Parmesan, and simmer over medium heat, stirring, until the sauce thickens, about 3–5 minutes.
Return the cooked chicken to the skillet and stir to coat with the sauce.
Add the drained penne to the skillet and toss everything together until evenly combined; cook 1–2 minutes to heat through.
Serve topped with the remaining Parmesan and chopped parsley.
