Heat olive oil in a large pot or deep skillet over medium-high heat.
Add the chicken pieces and cook for 5-6 minutes, stirring occasionally, until browned and cooked through. Remove chicken from the pot and set aside.
Reduce heat to medium. Add minced garlic to the pot and sauté for 1 minute until fragrant.
Pour in chicken broth and heavy cream. Stir to combine.
Add uncooked penne pasta, dried Italian seasoning, salt, and black pepper. Stir well.
Bring the mixture to a boil, then reduce heat to medium-low. Cover and simmer for 12-15 minutes, stirring occasionally, until pasta is tender and most of the liquid is absorbed.
Return the cooked chicken to the pot and stir in grated Parmesan cheese until melted and creamy.
Add chopped baby spinach and cook for an additional 2 minutes until spinach is wilted.
Remove from heat and stir in chopped fresh parsley.
Serve immediately.