In the bowl of a food processor combine the flour, butter, sugar and salt and process until the mixture resembles breadcrumbs. Add enough of the ice water, 1 tablespoon at a time, until the mixture forms a ball. Form a disk, wrap in plastic and refrigerate fo 20 minutes. Preheat the oven to 425F. In the base of a 10-inch heavy-bottomed tart pan or cast iron frying pan melt 1/4 cup of butter with 2/3 cup of the sugar. Arrange the apricot halves, rounded-side down in the butter-sugar mixture. Cook over a medium heat for 15 minutes. Sprinkle the remaining sugar over the apricots. Roll out the pie dough and place it over the apricots, tucking it in around the edges. Bake for 30-35 minutes. Remove the pan from the oven and cool for 10 minutes. Invert the pan onto a serving platter.
