How to Make It
In a medium bowl, toss the butter cubes with the 4 1/2 cups of flour and the granulated sugar. Refrigerate for 10 minutes.
In a small bowl, whisk the water with the vinegar and 2 1/2 teaspoons of the salt until the salt dissolves. Refrigerate for 10 minutes.
Transfer the flour mixture to a food processor. Pulse until the butter is in pea-size pieces. Drizzle in the vinegar water and pulse until moist crumbs form. Turn the dough out onto a work surface and knead lightly once or twice. Pat the dough into a 6-by-8-inch rectangle and then cut the dough into quarters. Wrap each quarter in plastic wrap and refrigerate until firm, about 1 hour.
In a small saucepan, combine the strawberries with the strawberry jam and the cornstarch slurry. Bring the filling to a boil over low heat, stirring frequently. Boil for 2 minutes, stirring constantly. Remove the saucepan from the heat and cool the filling at room temperature for 20 minutes, then refrigerate until thoroughly cooled, about 40 minutes longer.
Line two baking sheets with parchment paper. On a lightly floured work surface, roll out one fourth of the chilled dough to a 9-by-10-inch rectangle about 1/8 inch thick. Cut the dough into six 3-by-5-inch rectangles. Transfer the rectangles to one of the prepared baking sheets. Repeat with the remaining dough.
In a small bowl, lightly beat the egg with 2 tablespoons of water. Brush 12 of the rectangles with the egg wash and spread 1 tablespoon of the strawberry filling in the center of each one, leaving a 1/2-inch border all the way around. Top with a second rectangle of dough. Press the edges to seal and crimp with a floured fork. Prick the top of each pop tart a few times with a fork. Refrigerate until the dough is firm, 20 minutes.
Preheat the oven to 350°. Bake the pop tarts in the middle and lower thirds of the oven for 35 minutes, until the pastry is golden brown; shift the pans from top to bottom and front to back halfway through baking. Transfer the pop tarts to a rack and cool completely.
Make the frosting In a medium bowl, whisk the confectioners’ sugar with the milk, vanilla and the remaining 1/4 teaspoon salt until smooth. Spread 2 tablespoons of the icing on each cooled pop tart and decorate with the sprinkles before the icing sets.