Pat the chicken breasts dry with paper towels and season both sides generously with salt and black pepper. If your chicken breasts are very thick, you can slice them in half horizontally to create thinner cutlets.

Heat the olive oil and butter in a large skillet over medium-high heat. Once the butter has melted and the oil is shimmering, carefully place the seasoned chicken breasts into the hot skillet. Cook for about 5-7 minutes per side, or until golden brown and cooked through. The internal temperature should reach 165°F (74°C). Once cooked, remove the chicken from the skillet and set it aside on a plate. Tent it loosely with foil to keep warm.

Reduce the heat to medium. In the same skillet, add the minced garlic. Cook for about 1 minute, stirring constantly, until fragrant. Be careful not to burn the garlic.

Pour the heavy cream into the skillet with the garlic. Bring it to a gentle simmer and let it simmer for 2-3 minutes, allowing it to thicken slightly.

Stir in the grated Parmesan cheese until fully melted and the sauce is smooth and creamy. Taste the sauce and adjust seasoning with salt and pepper if needed.

Return the cooked chicken breasts to the skillet, nestling them into the sauce. Spoon some of the sauce over the top of each chicken breast and let it simmer for another 1-2 minutes.

Remove the skillet from heat, garnish with chopped parsley and extra grated Parmesan, if desired, and serve immediately.