In a large skillet, heat the olive oil over medium-high heat. Season the chicken breasts with salt and pepper. Add the chicken to the skillet and cook for about 6-7 minutes on each side until golden brown and cooked through. Remove the chicken from the skillet and set aside.
In the same skillet, reduce the heat to medium and add the minced garlic. Sauté for about 1 minute until fragrant, being careful not to burn it.
Pour in the chicken broth and bring to a simmer, scraping up any browned bits from the bottom of the skillet.
Stir in the heavy cream and Italian seasoning, then let the mixture simmer for about 3-4 minutes until it thickens slightly.
Add the grated Parmesan cheese to the skillet and stir until melted and well combined.
Return the cooked chicken to the skillet, spooning the sauce over the top. Let it simmer for an additional 2-3 minutes to heat the chicken through.
Garnish with chopped parsley before serving.