To make the pie crust, combine the flour and butter in a food processor until the mixture resembles breadcrumbs. Add the remaining ingredients and when the mixture forms a ball, make a disk, wrap it in plastic and refrigerate for 30 minutes. Preheat the oven to 450F. In a 10-inch cast-iron frying pan melt the butter and 2/3 cup of the sugar. Place the apple quarters in the pan rounded-side down. Add the vanilla. Over a moderately high heat, cook until the butter-sugar mixture caramelizes and becomes a rich golden-brown color. Roll out the dough to a 1/4-inch thick and place it over the apples, tucking it in around the edges. Prick the pie crust in several places with a fork. Bake for 20-25 minutes, until the crust is golden-brown. Rest the pan for 10 minutes after removing it from the oven. Invert the pan over a serving platter. Serve warm or at room temperature.
