To make the crust: Mix the flour, sugar, and salt in a processor. Add the butter. Pulse until the mixture resembles a coarse meal. Add the ice water and pulse until moist clumps form. Gather the dough into a ball; flatten into a disk. (If the dough still crumbles and does not form into a ball, add another tablespoon of ice water.) Wrap the dough in plastic and refrigerate until firm, about 1 hour.
For the filling: Position the rack in the center of the oven and preheat the oven to 400 degrees F.
Combine the apples, 1/4 cup of sugar, and lemon juice in large bowl; toss gently to blend. Set aside for 10 minutes.
Meanwhile, dust a large sheet of parchment paper with flour and roll out the dough on the paper to an 11-inch round. Transfer the dough on the parchment paper to a heavy large baking sheet. Spoon the apple mixture over the dough, leaving a 2-inch border. Fold the dough border over the filling to form an 8-inch round, leaving the apples exposed in the center. Pleat loosely and pinch the dough to seal any cracks. Brush the crust with the egg wash and sprinkle with the remaining 1 tablespoon of sugar.
Bake the crostata until the crust is golden and the apples are tender, about 40 minutes. Transfer the baking sheet to a rack; cool for 10 minutes. Slide a metal spatula under the crust to free the crostata from the baking sheet. Cool the crostata to lukewarm. Sprinkle with the almonds and serve.