Pound Chicken to Even Thickness:
Using a meat mallet or rolling pin, pound each chicken breast to a uniform thickness of about ½ inch. Pat the meat dry with paper towels.Dredge in Seasoned Flour:
On a plate, mix together the flour, salt, and pepper. Dredge each breast lightly in the seasoned flour, shaking off any excess.Sear Chicken Until Cooked:
In a large frying pan over medium-high heat, warm 3 tablespoons of butter and the olive oil until shimmering. Add the chicken and sear on both sides, roughly 4–5 minutes per side, until fully cooked. Move the cooked breasts to a plate and tent loosely with foil to keep warm.Sauté Garlic in Butter:
Lower the heat to medium. Melt the remaining 3 tablespoons of butter in the same pan. Add the minced garlic and sauté just until aromatic, about 30–60 seconds.Deglaze with Wine and Stock:
Pour in the white wine and chicken stock, using a wooden spoon to deglaze the pan by scraping up any browned bits. Allow the liquid to simmer and reduce for a few minutes.Add Cream and Parsley:
Add the heavy cream and chopped parsley, stirring to combine. Let the sauce simmer gently until it thickens slightly and turns glossy. Adjust seasoning to taste if necessary.Return Chicken to Sauce:
Return the chicken to the pan, spooning the sauce over each piece. Warm the breasts for 1–2 minutes to let them absorb the sauce.Serve with Lemon Wedges:
Serve the chicken on plates, drizzle with additional sauce, and accompany with lemon wedges.