Slice 4 chicken breasts in half horizontally to create thin cutlets, and pound them to an even thickness.
In a shallow dish, mix ½ cup all-purpose flour, 1 teaspoon kosher salt, and ½ teaspoon freshly ground black pepper. Dredge the chicken in the mixture, shaking off any excess.
Heat 3 tablespoons olive oil in a large skillet over medium heat. Cook the chicken cutlets for 3-4 minutes per side, or until golden brown and cooked through. Remove from the skillet and set aside.
Make the Sauce:
In the same skillet, melt 2 tablespoons unsalted butter over medium heat. Add 3 minced garlic cloves and sauté until fragrant, about 1 minute.
Deglaze the pan with ¼ cup dry white wine (if using) and let it simmer for 2 minutes, scraping any browned bits from the bottom of the pan.
Add 1 cup chicken broth, ½ cup fresh lemon juice, and 1 tablespoon capers to the skillet. Simmer for 3-4 minutes to reduce slightly.
Reduce the heat to medium-low and stir in ¼ cup heavy cream. Let the sauce simmer gently for 2-3 minutes, stirring occasionally, until it thickens slightly.
Return Chicken to the Pan:
Place the chicken back into the skillet, spooning the creamy lemon sauce over the top. Let it simmer for another 2-3 minutes to absorb the flavors.
Garnish and Serve:
Sprinkle with 2 tablespoons fresh parsley and 1 tablespoon fresh thyme leaves. Garnish with lemon slices for a pop of color. Serve hot.