Step 1: Pat chicken breasts dry with paper towels and season generously with salt and black pepper on both sides. If chicken breasts are thick, slice them in half horizontally or pound them to about 1/2-inch thickness for even cooking.
Step 2: Heat 1 tablespoon of olive oil in a large oven-safe skillet (cast iron or stainless steel recommended) over medium-high heat. Once shimmering, add the chicken breasts and sear for 3-4 minutes per side until golden brown. Remove chicken from the skillet and set aside.
Step 3: Reduce heat to medium. Add the remaining 1 tablespoon of olive oil and the unsalted butter to the same skillet. Add the minced garlic and sauté for about 1 minute until fragrant, being careful not to burn it.
Step 4: Pour in the chicken broth and fresh lemon juice. Bring to a simmer, scraping up any browned bits from the bottom of the pan with a wooden spoon. This deglazes the pan and adds flavor to the sauce.
Step 5: Stir in the heavy cream and bring to a gentle simmer. Cook for 2-3 minutes, allowing the sauce to thicken slightly. Reduce the heat to low, then gradually stir in the freshly grated Parmesan cheese until it's fully melted and the sauce is smooth and creamy. Stir in the red pepper flakes, if using. Taste and adjust seasoning if needed.
Step 6: Return the seared chicken breasts to the skillet, nestling them into the creamy sauce. You can either cover the skillet and continue to cook on the stovetop over low heat for 5-8 minutes, or transfer the skillet to a preheated oven at 375°F (190°C) and bake for 8-12 minutes, or until the chicken reaches an internal temperature of 165°F (74°C).
Step 7: Garnish with fresh chopped parsley and an extra sprinkle of Parmesan cheese before serving. Serve hot with your favorite sides.