In a medium bowl, whisk together the flour, sugar, and salt. Grate the cold butter into the mixture, then cut it in with a pastry cutter or fork until it resembles coarse crumbs.
1 cup all-purpose flour, 8 tablespoons unsalted butter, ½ teaspoon fine sea salt, 2 tablespoons sugar
Add the sourdough discard and vinegar. Stir with a fork until the dough begins to come together, then use your hands to shape it into a ball. Form into a rectangle, wrap in plastic wrap, and chill for at least 1 hour (up to 24 hours).
½ cup sourdough discard, 1 teaspoon apple cider vinegar
Preheat the oven to 350°F (180°C). Line a baking sheet with parchment paper.
On a lightly floured surface, roll the dough into a rectangle about ⅛ inch thick. Cut into 4 long strips. Brush the edges with egg wash.
Place 2 tablespoons of jam on one side of each strip, then fold over. Press the edges with a fork to seal and brush the tops with more egg wash.
½ cup strawberry jam, 1 egg
Transfer to the baking sheet and bake for 25–30 minutes, until golden brown. Cool on a wire rack.
Whisk together powdered sugar and water until smooth. Drizzle over cooled pop tarts and decorate with coarse sugar or sprinkles if desired.
½ cup powdered sugar, 1 teaspoon water