Season the chicken pieces with Italian seasoning, 1 teaspoon salt, and pepper.

In a large skillet, heat avocado oil over medium heat. Add the seasoned chicken pieces and cook until browned and cooked through, about 6-8 minutes. Remove the chicken from the skillet and set aside.

In the same skillet, add diced onion and cook until softened and translucent, about 5 minutes.

Add minced garlic, sun-dried tomatoes, dried basil, dried thyme, and the remaining 1 teaspoon salt to the skillet. Stir constantly to ensure the herbs evenly combine and do not clump. Cook for an additional 1-2 minutes until fragrant.

Pour in the chicken broth and 2 cups heavy cream, and bring the mixture to a simmer. Simmer for 5 minutes, or until the sauce begins to thicken slightly.

Stir in the grated Parmesan cheese. Continue to simmer, stirring frequently, until the cheese has melted and the sauce has thickened to your desired consistency, about 3-4 minutes.

Return the cooked chicken to the skillet, stirring to coat the chicken in the sauce. Add the cooked penne pasta and toss to combine.

Pour in the remaining 1/2 cup of heavy cream, stirring gently to coat the pasta and chicken evenly. Let it simmer for another 2-3 minutes, just until the sauce thickens and everything is heated through.

Serve immediately. Garnish with additional grated Parmesan cheese, if desired.