Step 1: In a large mixing bowl, whisk together the all-purpose flour, 1 teaspoon granulated sugar, and salt.
Step 2: Add the very cold, cubed unsalted butter to the flour mixture. Using a pastry blender, your fingertips, or a food processor, cut the butter into the flour until the mixture resembles coarse crumbs with some pea-sized pieces of butter remaining.
Step 3: Gradually add ice-cold water, one tablespoon at a time, mixing lightly until the dough just comes together. Be careful not to overmix. The dough should be shaggy but cohesive.
Step 4: Divide the dough in half, flatten each half into a disc, wrap tightly in plastic wrap, and refrigerate for at least 30 minutes, or up to 2 days.
Step 5: In a medium saucepan, combine the elderberries, ½ cup granulated sugar, lemon juice, and cornstarch.
Step 6: Cook over medium heat, stirring constantly, until the mixture thickens and the elderberries soften, about 5-7 minutes. Remove from heat and let it cool completely.
Step 7: Preheat your oven to 375°F (190°C). Line a baking sheet with parchment paper.
Step 8: On a lightly floured surface, roll out one disc of chilled dough to about 1/8-inch thickness. Using a 3-4 inch round or square cutter, cut out even shapes. Repeat with the second dough disc.
Step 9: Spoon about 1-2 tablespoons of the cooled elderberry filling onto one half of each pastry cutout, leaving a small border around the edge.
Step 10: Fold the other half of the pastry over the filling. Press the edges together firmly to seal and use a fork to crimp them. Cut a few small slits on the top of each pie.
Step 11: Whisk the egg with a tablespoon of water to create an egg wash. Brush the tops of the assembled hand pies with the egg wash and sprinkle with coarse sugar, if desired.
Step 12: Place the hand pies on the prepared baking sheet and bake for 20-25 minutes, or until the crust is golden brown and the filling is bubbling.
Step 13: Let the hand pies cool on a wire rack for at least 15-20 minutes before serving. Enjoy warm or at room temperature!