Slice chicken breasts in half horizontally to create thinner cutlets. Season both sides with salt and pepper.
Heat olive oil and butter in a large skillet over medium-high heat.
Add chicken to the skillet and cook for 5-7 minutes per side, until golden brown and cooked through (internal temperature reaches 165°F or 74°C). Remove chicken and set aside.
Reduce heat to medium. Add minced garlic to the same skillet and cook for about 1 minute until fragrant. Do not let it burn.
Pour in chicken broth and scrape up any browned bits from the bottom of the pan. Let it simmer for 2 minutes.
Stir in heavy cream and Italian seasoning. Bring the sauce to a gentle simmer.
Reduce heat to low and gradually stir in the grated Parmesan cheese until the sauce is smooth.
Return the cooked chicken to the skillet. Spoon the sauce over the chicken.
Simmer for 2-3 minutes to heat the chicken through and allow the sauce to thicken slightly.
Garnish with fresh parsley before serving.
Notes
For a brighter flavor, add 1 tablespoon of fresh lemon juice to the sauce when you add the heavy cream.
If you prefer thicker chicken breasts, pound them to an even thickness before cooking to ensure even cooking time.
Serve this dish over pasta, rice, or with steamed vegetables.