Season the chicken cutlets with salt and pepper.
Lightly dredge the cutlets in flour, coating them evenly.
Heat a sauté pan over medium-high heat with vegetable oil.
Add the chicken cutlets and cook for 2 to 3 minutes until golden brown.
Flip the cutlets, cover the pan, and cook for 1 to 2 minutes until cooked through.
Transfer the chicken to a warm plate and cover to keep warm.
Pour off excess fat from the pan.
Add the dry white wine and deglaze the pan, scraping up any browned bits.
Add the minced garlic and cook until lightly browned and most of the liquid has evaporated.
Pour in the chicken broth, lemon juice, and drained capers.
Return the chicken cutlets to the pan and cook for about 1 minute per side.
Add the unsalted butter and lemon slices, allowing the butter to melt and form a sauce.
Spoon the sauce over the chicken and garnish with chopped fresh parsley before serving.