If your chicken breasts have tenderloins attached, remove them and reserve for another use. Place the breasts between 2 sheets of plastic wrap and gently pound them to a uniform thickness of 1/2-inch.
Combine the flour with 1 teaspoon of salt and a few grinds of black pepper and spread on a plate. Dredge the chicken in the flour, shaking off any excess.
Heat the olive oil in an oven-proof frying pan over medium-high heat. Add the chicken in a single layer and cook until lightly browned, 2 to 3 minutes per side. Remove from the heat.
Combine the cream, wine and Dijon-style mustard in a small bowl. Season with a bit of salt and pepper, then taste and add more mustard if desired.
Spread the mixture evenly over the chicken then top with shredded cheese and finish with the panko crumbs. Bake until the cheese is bubbly and the crumbs are lightly toasted, 12 to 15 minutes. Sprinkle with parsley if desired and serve immediately.