Trim any excess fat from the chicken breasts and slice them in half lengthwise to make two thin cutlets. Season both sides of the chicken breasts evenly with the kosher salt and freshly ground black pepper then dredge each breast in the all-purpose flour, shaking off any excess.
Heat butter with the extra virgin olive oil in a large skillet over medium-high heat. Add the chicken and cook for 3-4 minutes per side or until golden brown. Transfer to a platter or sheet pan and cover with foil.
Reduce the heat to medium, add the garlic, and cook until fragrant, about 1 minute. Sprinkle the garlic with the remaining tablespoon of flour, stirring while you cook for 1 minute.
Whisk in the chicken stock, lemon juice, and heavy cream, scraping up the browned bits from the pan.
Add the sliced lemon and cook for 4-5 minutes until the cream sauce thickens.
Stir in the remaining 1 tablespoon of butter until melted. Add the chicken back to the sauce. Taste for seasoning and top with parsley or fresh thyme if desired.
