How to Make It
Preheat oven to 425°F. Place Honeycrisp apple; cranberries; light brown sugar; and kosher salt in a medium saucepan. Cook over medium-high, stirring often, until apple is tender and cranberries burst, about 8 minutes.
Whisk together cornstarch and water in a small bowl, and stir into apple mixture. Bring to a boil over medium-high, stirring often; cook until mixture thickens, about 1 minute. Transfer to a medium bowl; stir in unsalted butter, vanilla extract, and ground nutmeg. Let cool at room temperature until butter is melted and mixture has thickened, about 20 minutes. Stir cooled mixture, and set aside.
Unroll 1 piecrust from a package of refrigerated piecrusts; cut into 4 (4-inch) squares. Reroll remaining dough; cut into 2 additional (4-inch) squares. Repeat procedure with remaining 1 piecrust.
Arrange squares evenly on 2 baking sheets lined with parchment paper. Place 1 heaping Tbsp. cooled apple mixture in center of each square. Fold corners of square in toward center, pressing (or twisting) gently to seal together. Brush tartlets with egg white, and sprinkle with demerara sugar.
Bake in preheated oven until golden and bubbly, 14 to 16 minutes. Cool on baking sheets on wire racks 15 minutes. Serve warm or at room temperature.