Cook the penne pasta according to package instructions until al dente. Drain and set aside.
In a large skillet, heat the olive oil over medium heat. Add the minced garlic and sauté for about 1 minute until fragrant.
Pour in the heavy cream and chicken broth, stirring to combine. Bring the mixture to a gentle simmer.
Add the shredded rotisserie chicken, Italian seasoning, salt, and pepper. Stir well and let it cook for about 5 minutes.
Gradually add the grated Parmesan cheese, stirring until melted and the sauce is creamy.
Fold in the fresh spinach and cooked penne pasta. Stir until the spinach wilts and everything is well combined.
Remove from heat and garnish with chopped parsley if desired. Serve warm.