Begin by seasoning the chicken breasts generously with salt and black pepper on both sides to ensure the chicken is flavorful. Heat olive oil in a large skillet over medium-high heat. Once the oil is hot, add the chicken breasts and sear them for 4-5 minutes on each side until golden brown. At this stage, the chicken doesn't need to be fully cooked since it will finish cooking in the sauce later.

After searing the chicken, remove it from the skillet and set it aside on a plate. Add butter to the same skillet and let it melt. Once melted, add the minced garlic and sauté for about 1 minute. Be cautious during this step as garlic can burn quickly, resulting in a bitter flavor. Stir frequently to ensure it cooks evenly.

Pour chicken broth into the skillet, using a wooden spoon or spatula to scrape up the browned bits left from searing the chicken. These bits add extra flavor to the sauce. Reduce the heat to low-medium, then slowly whisk in heavy cream, ensuring it combines well. Add Parmesan cheese and stir until it's fully melted, creating a smooth and creamy sauce that will coat the chicken beautifully.

Return the chicken breasts to the skillet, ensuring they’re submerged in the creamy garlic sauce. Let the dish simmer on low for about 10 minutes, allowing the chicken to fully cook. The chicken's internal temperature should reach 165°F. Once cooked, garnish the dish with freshly chopped parsley for a burst of color and added freshness to the rich creamy sauce.