Pulse flour, salt, and sugar in a food processor. Add butter and continue to pulse until the mixture resembles coarse sand. With the motor running, add 6 tablespoons of cold water and process until dough comes together, 30 seconds to 1 minute.
Divide dough in half and form into disks; wrap disks separately in plastic wrap and refrigerate for 1 hour.
Preheat oven to 425°F On a lightly floured surface, roll 1 disk of dough into a 9" square. Cut into six 3" x 4.5" rectangles; transfer to a parchment-lined baking sheet.
Spread each rectangle with about 1 tablespoon goat cheese and top with 1 tablespoon jam, leaving a 1/2" border; set aside. Repeat rolling and cutting with remaining disk of dough and lightly prick dough with a fork.
Brush edges of dough around cheese and jam with beaten egg and top with pricked dough rectangles. Using the tines of a fork, press edges to seal. Bake until puffed and golden, about 15 minutes. Transfer tarts to a baking sheet with a wire rack; let cool completely.
Whisk confectioners' sugar, strawberries and 2 tablespoons water until smooth. Drizzle over tops of tarts and let sit until glaze is completely set.