Begin by seasoning the chicken breasts generously with salt on both sides.
In a large skillet, heat olive oil over medium-high heat until shimmering. Carefully add the seasoned chicken breasts and sauté them for approximately 6-7 minutes on each side until they turn golden brown and are cooked through.
Once the chicken is fully cooked, transfer it to a plate and cover it with foil to keep warm while you prepare the sauce.
In the same skillet, reduce the heat to medium and add unsalted butter; let it melt completely before pouring in heavy cream. Stir continuously as you add in grated Pecorino Romano cheese along with freshly cracked black pepper until everything is well combined and smooth.
Return the sautéed chicken breasts back into the skillet, ensuring they are thoroughly coated in the creamy sauce. Allow them to simmer together for an additional 2-3 minutes so that all flavors meld beautifully.
Taste your sauce before plating; adjust seasoning with more salt if needed. Place each chicken breast on a serving plate, spoon additional sauce over them, and finish with extra black pepper and chopped fresh parsley as garnish before serving warm alongside your favorite sides.