Cube butter, and freeze for 30 minutes.

In the work bowl of a food processor, place flour and 2¼ teaspoons (6.75 grams) salt; pulse until combined. Add frozen butter; pulse until butter is dime-size. With processor running, add ½ cup (120 grams) ice water in a slow, steady stream just until dough comes together and forms a ball. Turn out dough onto a lightly floured surface; shape into a 6-inch square. Wrap in plastic wrap, and refrigerate for at least 30 minutes.

On a lightly floured surface, roll dough into a 15×7½-inch rectangle, lightly flouring surface as needed to prevent sticking. Fold dough in thirds, like a letter, and turn 90 degrees. Repeat procedure twice. Wrap in plastic wrap, and refrigerate for at least 20 minutes

Line 2 baking sheets with parchment paper.

Divide dough in half. On a lightly floured surface, roll 1 portion into a 12×9-inch rectangle, lightly flouring surface and dough as needed to prevent sticking. Using a pastry wheel, cut dough into 9 rectangles (about 4×3 inches each). Place evenly spaced on a prepared pan, and refrigerate; repeat procedure with remaining dough.

Preheat oven to 350°F (180°C).

In a small bowl, stir together sweet potato, brown sugar, vanilla, cinnamon, ginger, nutmeg, and remaining ⅛ teaspoon salt; divide sweet potato mixture among 9 dough rectangles (about 2½ teaspoons [16 grams] each); using a small offset spatula, spread sweet potato mixture evenly within each rectangle, leaving a ¼- to ½-inch border around edges. Brush egg onto border of each rectangle; top each with a second dough rectangle. Using the tines of a fork, crimp edges to seal each pastry pocket; brush egg onto dough, and poke tops 3 to 4 times with tines of fork. Using a small sharp knife, trim rectangles to create cleaner edges, if desired.

Bake until puffed and golden brown, 20 to 25 minutes. Let cool on pans for at least 10 minutes. Just before serving, spoon and spread Cinnamon-Brown Sugar Glaze onto hand pies, working quickly. Garnish immediately with turbinado sugar, if desired. Serve warm or at room temperature.