Pound the chicken cutlets to 1/4-inch thickness, season with salt and pepper, and dredge in all-purpose flour.

Heat vegetable oil in a sauté pan over medium-high heat. Cook the chicken for 2-3 minutes on the first side until golden brown, then flip, cover, and cook for 1-2 minutes more until cooked through. Remove to a warm plate and tent with foil.

Pour off any excess fat from the pan. Deglaze with dry white wine, scraping up the browned bits. Add minced garlic and cook until slightly browned and the liquid is nearly evaporated, about 2 minutes.

Add chicken broth, fresh lemon juice, and capers. Return the chicken to the pan and simmer for about 1 minute on each side.

Add unsalted butter and fresh lemon slices, swirling the pan until the butter melts. Pour the sauce over the chicken, garnish with chopped parsley, and serve immediately.