Step 1

In a medium saucepan, whisk together the sugar and cornstarch.

Step 2

Pour in 1/2 cup water and whisk until combined. Whisk in the rum, orange zest, vanilla extract or paste, and salt. Add the thyme sprig. Set the saucepan over medium heat and cook, whisking constantly, until the mixture is reduced and syrupy, 12 to 15 minutes.

Step 3

Remove from the heat and gently stir in the blueberries. Let stand for 30 minutes.

Step 4

Remove and discard the thyme sprig from the blueberries. Divvy the piecrust in half. Cover and refrigerate 1 portion until ready to use. On a lightly floured surface, roll out the remaining portion to 1/8-inch (3-mm) thickness on a lightly floured surface. Cut the dough into 10 circles with a 4 1/2-inch (11-cm) round cookie cutter gently rerolling the dough scraps once and cutting out more rounds. Repeat with the remaining dough half.

Step 5

Spoon about 1 tablespoon filling into the center of each dough circle. Whisk together the egg and remaining 1/4 cup water. Brush the edges of each pie and fold the dough over the filling so the edges meet. Press the edges together with a fork to seal, taking care to seal the sides together well to prevent leaking. Repeat the process with the remaining dough, filling, and egg wash. (You may end up with some extra filling. We highly encourage spooning it over vanilla ice cream. Or just scooping it up straight from the pan.)

Step 6

In a deep-sided skillet set over medium heat, warm the oil to 375°F (190°C). Place a couple layers of paper towels on a baking sheet and place alongside the stove. Fry the pies until golden brown, 2 to 4 minutes. Turn and cook 2 minutes longer. Use a slotted spatula to move the pies to paper towels. Let cool for 20 minutes.

Step 7

In a small bowl, whisk together the confectioners’ sugar and lemon juice. Slowly whisk in the cream, 1 teaspoon at a time, until the desired consistency is reached.

Step 8

Drizzle the glaze over the pies and devour immediately.