In a medium saucepan, cook blackberries, honey, brown sugar, and butter over medium heat, stirring occasionally, until blackberries start to brighten in color and release their juices, about 3 minutes.
In a small bowl, whisk together cornstarch and 2 tablespoons (30 grams) water until smooth; using a rubber spatula, stir into blackberry mixture. Cook, stirring constantly, until thickened, about 1 minute. Transfer to a heatproof bowl, and let cool slightly, 15 to 20 minutes. Cover with a piece of plastic wrap, pressing wrap directly onto surface of mixture to prevent a skin from forming, and refrigerate until completely cool.
In another small bowl, whisk together egg and remaining 2 teaspoons (10 grams) water.
On a lightly floured surface, roll Hand Pie Dough to ⅛-inch thickness. Using a 4-inch round cutter, cut dough, gently rerolling scraps once. Spoon 1 heaping tablespoon blackberry mixture in center of each dough circle. Brush edges of dough with egg wash. Fold dough in half to cover filling, and cup in the palm of your hand. Press edges tightly together to seal, pushing air out from center of pies; press edges with the tines of a fork. Place on a parchment paper-lined baking sheet; freeze for 30 minutes, or refrigerate for1 hour.
In a large Dutch oven, pour oil to a depth of 1½ inches, and heat over medium-high heat until a deep-fry thermometer registers 350°F (180°C).
Fry pies in batches, turning occasionally, until golden brown, 3 to 4 minutes. Let drain on paper towels. Sprinkle with granulated sugar, and serve immediately, or let cool completely, and dust with confectioners’ sugar.