Heat olive oil in a large skillet over medium-high heat.
Season chicken pieces with salt and black pepper.
Add chicken to the skillet and cook for 5-6 minutes, stirring occasionally, until golden brown and cooked through. Remove chicken from skillet and set aside.
Reduce heat to medium and add minced garlic to the same skillet. Cook for 1 minute until fragrant, stirring constantly to prevent burning.
Pour in chicken broth and heavy cream, stirring to combine.
Add uncooked penne pasta, dried Italian seasoning, and crushed red pepper flakes to the skillet. Stir well.
Bring the mixture to a boil, then reduce heat to low. Cover and simmer for 12-15 minutes, stirring occasionally, until pasta is tender and most of the liquid is absorbed.
Stir in grated Parmesan cheese until melted and sauce is creamy.
Return cooked chicken to the skillet and add fresh baby spinach leaves. Stir until spinach wilts, about 2 minutes.
Remove from heat and sprinkle chopped fresh parsley over the pasta.
Serve immediately.