In large bowl, toss the potatoes with butter, olive oil, season salt, cayenne, parsley and 3 Tablespoons Parmesan cheese, if desired.
Arrange in a single layer on 2 cookie sheets. Bake until golden brown and crisp, about 45 minutes. About half way through baking, flip potatoes using a flat spatula.
Remove from oven and taste for seasoning. Add kosher salt to taste and transfer to a serving platter. Garnish with more Parmesan cheese and serve.