Prepare the Chicken
Place each chicken breast between two sheets of plastic wrap and gently pound to an even thickness of about ½ inch.
Pat the chicken dry with paper towels.
Season and Coat
In a shallow dish, combine the flour, salt, and black pepper.
Lightly dredge each chicken breast in the seasoned flour, shaking off any excess.
Cook the Chicken
Heat 3 tablespoons of butter and the olive oil in a large skillet over medium-high heat.
Once hot and shimmering, add the chicken breasts.
Cook for 4–5 minutes per side, or until golden brown and cooked through.
Transfer the chicken to a plate and loosely cover with foil to keep warm.
Make the Garlic Cream Sauce
Reduce the heat to medium.
Add the remaining 3 tablespoons butter to the skillet.
Stir in the minced garlic and cook for 30–60 seconds until fragrant.
Deglaze the Pan
Pour in the white wine and chicken stock.
Scrape up the browned bits from the bottom of the skillet using a wooden spoon.
Allow the liquid to simmer and reduce slightly for 2–3 minutes.
Finish the Sauce
Stir in the heavy cream and chopped parsley.
Simmer gently for 3–5 minutes until the sauce thickens slightly and becomes silky.
Taste and adjust seasoning if needed.
Combine and Serve
Return the chicken breasts to the skillet.
Spoon the sauce over the chicken and cook for 1–2 minutes until heated through.
Transfer to serving plates and generously spoon extra sauce over each piece.
Serve immediately with fresh lemon wedges.