Flatten each chicken breast to an even thickness using a meat mallet or rolling pin (about ½-inch). Pat the meat dry.

Combine the flour, salt, and pepper on a plate. Lightly coat each breast in the seasoned flour, tapping off any loose flour.

Heat 3 tablespoons of butter with the olive oil in a large frying pan over medium-high heat until shimmering.

Add the chicken and brown on both sides, about 4–5 minutes per side, until cooked through. Transfer the cooked breasts to a plate and cover loosely to keep warm.

Reduce the heat to medium. Add the remaining 3 tablespoons of butter to the same pan. Once melted, add the minced garlic and cook very briefly—just until fragrant (about 30–60 seconds).

Pour in the white wine and chicken stock, using a wooden spoon to scrape up the browned bits from the bottom of the pan. Let the liquid bubble and reduce for a couple of minutes.

Stir in the heavy cream and chopped parsley, simmering gently until the sauce thickens a little and becomes glossy. Taste and adjust seasoning if needed.

Return the chicken to the pan and spoon the sauce over each piece, warming the breasts through for a minute or two so they soak up the sauce.

Plate the chicken, spoon extra sauce over top, and serve with lemon wedges alongside.