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 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 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.