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

In a plate, combine the flour, salt, and pepper. Lightly coat each breast in the seasoned flour, tapping off any excess.

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

Add the chicken and brown on both sides, about 4–5 minutes per side, until cooked through. Once done, transfer the chicken to a plate and 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 stir just until fragrant (30–60 seconds).

Pour in the white wine and chicken stock, using a wooden spoon to scrape up those delicious browned bits. Let it bubble and reduce for a couple of minutes.

Stir in the heavy cream and chopped parsley, letting it simmer until the sauce thickens and becomes glossy. Taste and season as needed.

Return the chicken to the pan, spoon the sauce over each piece, and warm the breasts through for a minute or two to soak up that flavor.

Plate the chicken, drizzle extra sauce on top, and serve with lemon wedges on the side.