Place each chicken breast between plastic wrap and gently pound with a meat mallet or rolling pin to about ½-inch thickness. Pat dry with paper towels.

On a plate, mix the flour with the salt and pepper. Lightly coat each breast in the seasoned flour, shaking off excess.

In a large frying pan over medium–high heat, heat 3 tablespoons of the butter with the olive oil until shimmering.

Add the chicken and cook undisturbed until golden brown, about 4–5 minutes per side, until an instant-read thermometer registers 165°F (74°C). Transfer to a plate and loosely tent with foil to keep warm.

Reduce heat to medium. Add the remaining 3 tablespoons butter to the pan. Once melted, add the minced garlic and cook just until fragrant, about 30–60 seconds—don’t let it brown.

Pour in the white wine and the chicken stock, using a wooden spoon to scrape up browned bits (fond) from the pan bottom. Let it bubble and reduce for 2–3 minutes.

Stir in the heavy cream and chopped parsley. Simmer gently until the sauce thickens slightly and shines. Taste and adjust seasoning with salt and pepper.

Return the chicken to the pan and spoon sauce over each piece. Warm through for 1–2 minutes.

Plate the breasts, spoon extra sauce over top, and offer lemon wedges for squeezing.