To make the dough, place flour, salt, and sugar in the bowl of a food processor, and pulse a few seconds to combine. Add cubed butter and pulse until the mixture resembles a coarse meal with a number of pea-sized bits, about 15 seconds. Add ice water in a slow drizzle through the feed tube, pulsing to incorporate. Check to see if dough holds together: remove processor lid and squeeze a bit of dough between your index finger and thumb. If it is crumbly it isn’t quite ready – drizzle a little more water while pulsing. If it holds together, it is ready. Do not process for more than 30 seconds or you will overwork the dough.
Lay two segments of cellophane on your work surface. Turn the dough out into two even piles. With each pile, gather either side of cellophane and use it to press dough into the center, into a ball. Securely wrap it and flatten into a disc. Repeat with the remaining dough. Refrigerate for at least a half hour to allow the flavor to mellow. Save a disc for another use – if tightly wrapped, dough will keep in the freezer up to one month.
In a large bowl, combine filling ingredients. With a rubber spatula, gently stir ingredients to incorporate, then let sit for 20 minutes.
Roll dough out on a sheet of lightly floured parchment to ⅛-inch thick. Use the parchment to transfer dough to a baking sheet and chill in the refrigerator if it has become soft or flabby. Bonus, you will keep the dough on this parchment to bake the crostada.
Spoon peach-black pepper mixture into center of dough, leaving a 3-inch border. Fold pastry over fruit mixture, pleating it as you work your way around. Use a small bit of water to seal dough pleats together. Brush pastry with egg wash. Sprinkle pastry with demerara sugar. Chill in refrigerator (or freezer) for at least one hour, up to overnight. The colder your pastry, the better assurance you have that it will stay as you have made it once in the oven.
Preheat oven to 425°. Bake crostada until crust is golden, checking after 25 minutes and rotating if needed. Lower heat to 400° if crust becomes darker than to your liking, and continue baking until juices bubble, about 15-25 minutes more. Cool completely on a wire rack. Crostada is delicious warm or room temperature, and will keep covered in foil room temperature for 2 days, refrigerated for 5.