Place the chicken breasts between two sheets of plastic wrap and pound them to an even thickness. Season both sides with salt and pepper.

Dredge the chicken in flour, shaking off the excess.

In a large skillet, melt the butter over medium heat. Add the chicken and cook until golden brown on both sides, about 4 minutes per side.

Remove the chicken from the skillet and place on a plate. Top each piece with two slices of prosciutto and a generous amount of grated gruyère.

Pour the white wine into the skillet and bring to a simmer, scraping up any browned bits from the bottom.

Return the chicken to the skillet and cover. Cook until the cheese is melted and the chicken is cooked through, about 8 minutes.

Garnish with chopped parsley and serve immediately.