In the work bowl of a food processor, place 2½ cups of all-purpose flour, 1½ tablespoons of granulated sugar, and ¾ teaspoon of kosher salt; pulse until combined. Add 1 cup of cold unsalted butter and pulse until the mixture is crumbly and butter is pea-sized. With the processor running, add 2 tablespoons of ice water slowly just until the dough comes together.
Turn out the dough and divide it in half, shaping each half into a 5-inch square. Wrap in plastic wrap and refrigerate until chilled, about 30 minutes.
In a small bowl, stir together 1 tablespoon of cornstarch and 1 tablespoon of water until well combined.
In a small saucepan, bring 1 cup of strawberry fruit spread to a boil over medium heat. Add the cornstarch mixture and cook until boiling and thickened slightly, about 10 to 12 minutes. Transfer to a bowl and refrigerate for at least 30 minutes.
Line 2 baking sheets with parchment paper. Roll half of the dough into a rectangle about 14 by 10 inches thick. Trim edges for a perfect rectangle and cut into 9 rectangles.
Transfer rectangles onto prepared pans, spoon a heaping tablespoon of chilled fruit spread mixture onto each, spreading it into a thin layer, leaving a ¾-inch border. Refrigerate until firm, about 10 minutes.
Roll out remaining dough and cut into another 9 rectangles. Dock them using a fork in ¼-inch intervals all over.
Whisk together 1 large egg and 1 tablespoon of water. Brush egg wash onto edges of chilled rectangles. Top with docked dough, pressing edges together firmly to seal.
Trim edges for a tight seal. Refrigerate until firm again, about 1 hour, or freeze for 15 minutes.
Preheat oven to 300°F (150°C). Bake until slightly puffed and golden brown, about 30 to 35 minutes. Cool on pans for 10 minutes before transferring to wire racks to cool completely.
In a medium bowl, whisk together 2 cups of confectioners’ sugar and 2½ tablespoons of water until smooth. Pipe a rectangle around edges of tarts, filling in the center. Garnish with sparkling sugar, if desired.
