Season chicken breasts with salt and pepper on both sides.
Heat olive oil in a large skillet over medium-high heat. Add chicken breasts and cook for 6-7 minutes per side until golden brown and cooked through. Remove chicken from skillet and set aside.
Add minced garlic to the skillet and sauté for about 30 seconds until fragrant.
Pour in chicken broth and scrape up browned bits from the bottom. Simmer for about 2 minutes.
Stir in heavy cream, Parmesan cheese, lemon juice, lemon zest, and dried Italian herbs. Whisk until cheese is melted.
Return chicken to the skillet, spoon some sauce over the top, and let it simmer for 3-4 minutes.
Sprinkle with chopped fresh parsley before serving.
