Pound chicken breasts to even thickness (about ½ inch). Season both sides with salt and 1 tsp black pepper.
Heat olive oil and butter in a skillet over medium-high heat. Add chicken and cook for 5–6 minutes per side until golden and cooked through (165°F internal temp). Transfer to a plate.
In the same skillet, sauté garlic for 30 seconds until fragrant. Pour in chicken broth to deglaze, scraping up browned bits.
Stir in heavy cream, Parmesan, and crushed peppercorns. Simmer for 3–4 minutes until slightly thickened.
Return chicken to the skillet, spooning sauce over it. Simmer for 2 more minutes.
Garnish with parsley and extra Parmesan. Serve over pasta, mashed potatoes, or with crusty bread.