Measure flour and salt (if including) into a bowl. Work half of butter into flour with your fingertips, lightly rubbing and breaking flour-coated pieces of butter into small bits until mixture is roughly the texture of oatmeal or cornmeal. Add remaining butter and work quickly into dough until pieces of butter are about half their original size.

Dribble water onto dough while tossing mixture with a fork. Keep adding water only until dough begins to clump and hold together, when you squeeze a handful. You may not need the entire ½ cup water. Divide dough in two and gather each part into a ball. Wrap each ball in plastic and flatten it into a disk. Let dough rest, refrigerated, about 1 hour. Freeze second disk of dough for future use, if desired.

Let dough warm up at room temperature for 15 minutes. Preheat oven to 400 degrees. Roll out dough on a lightly floured surface into a rough circle about 12 inches in diameter and ⅛ inch thick. Transfer pastry to a baking sheet lined with parchment paper and refrigerate while preparing apples.

Peel, core, and slice apples and toss with 1 to 2 tablespoons sugar and 1 teaspoon cinnamon. Arrange apples on pastry, in overlapping concentric circles or freely piled on top, leaving a 1 ½ inch border of dough around circumference. Fold dough up over apples and brush rim of dough lightly with egg. Sprinkle sugar over dough and apples; use more or less depending on the tartness of apples.

Bake in lower part of oven 45 to 50 minutes, until fruit is tender and pastry is golden brown and slightly caramelized at edges. Slide tart off pan to cool on a rack. Serve warm or at room temperature, with softly whipped cream, if desired.