Whisk the flour, sugar, and salt together in a large bowl, then cut in the cold, cubed butter using a pastry cutter until the mixture looks like coarse crumbs. Slowly add ice water, one tablespoon at a time, just until the dough comes together without being sticky. Shape it into two flat discs, wrap in plastic, and chill for at least 30 minutes.
While the dough chills, add the cherries, sugar, and lemon juice to a small saucepan over medium heat. Let them simmer for about five minutes until the cherries soften and release their juice. Stir in the cornstarch-water mixture and keep cooking until the filling thickens into a glossy, jammy consistency, then set it aside to cool completely.
On a lightly floured surface, roll one chilled dough disc into a rectangle about ⅛-inch thick. Trim the rough edges with a pizza cutter, then slice it into evenly sized rectangles, roughly 3x4 inches. Repeat with the second disc so you have a matching top and bottom for every tart.
Place half the rectangles on a parchment-lined baking sheet and spoon a tablespoon of cooled cherry filling onto the center of each, leaving a border around the edges. Brush the edges with egg wash, then top with a second rectangle of dough. Press the edges firmly and crimp with a fork to seal.
Brush the tops with the remaining egg wash and use a fork to poke a few small vents so steam can escape. Bake at 375°F for 18-20 minutes, until the pastry turns a deep golden brown. Let the tarts cool on the pan for a few minutes before moving them to a wire rack.
Once the pop tarts have cooled completely, whisk the powdered sugar with milk or a splash of reserved cherry juice until you have a smooth, pourable glaze. Drizzle it generously over each tart and let it set for a few minutes before serving.