If chicken breasts are thick, pound them to an even thickness.
Season chicken breasts with salt and pepper.
Heat olive oil in a large skillet over medium-high heat. Add chicken and cook for 6-8 minutes per side, or until cooked through and no longer pink in the center.
Remove chicken from the skillet and set aside.
Add butter to the skillet and melt over medium heat. Add minced garlic and cook until fragrant, about 1 minute.
Pour in chicken broth and heavy cream. Bring to a simmer and cook for 2-3 minutes, stirring occasionally, until the sauce thickens slightly.
Stir in grated Parmesan cheese and dried parsley until the cheese is melted and the sauce is smooth.
Return the chicken to the skillet and spoon the sauce over it. Let it simmer for another minute to warm through.
Serve immediately.
Notes
Serve with pasta, rice, or a side salad for a complete meal.