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Whisk together the sugar and cornstarch in a saucepan. Add 1⁄2 cup of the water, and whisk until combined. Whisk in the rum, orange zest, vanilla bean paste, and salt. Add the thyme sprig. Cook over medium, whisking constantly, until the mixture is thickened, 12 to 14 minutes. Remove from the heat, and fold in the blueberries. Let stand for 30 minutes. Remove and discard the thyme sprig.
Cut the piecrust in half. Refrigerate 1 portion until ready to use. Roll out remaining portion to 1⁄8-inch thickness on a lightly floured surface. Cut the dough into 10 circles with a 4 1⁄2-inch round cookie cutter, re-rolling scraps once. Repeat with remaining dough half.
Spoon about 1 tablespoon of filling into the center of each dough circle. Whisk together the egg and remaining 1⁄4 cup water. Brush the edges of the pies, and fold over so the edges meet. Press the edges together with a fork to seal. Repeat the process with the remaining dough, filling, and egg wash.
Heat the oil in a skillet over medium to 375°F. Fry the pies until golden brown, about 4 minutes. Turn and cook about 2 more minutes. Drain on paper towels, and let cool 20 minutes. Drizzle with Meyer Lemon Glaze.
Whisk together the powdered sugar and lemon juice in a small bowl. Whisk in the heavy cream, 1 teaspoon at a time, until desired consistency is reached. Makes 1⁄2 cup
Place the flour, sugar, and salt in the bowl of a food processor, and pulse a few times until combined. Add the butter and shortening, and pulse until the mixture resembles small peas, 8 to 12 times.
With the processor running, drizzle 6 tablespoons of the ice water through the food chute, and process until the dough begins to form a ball. (Add up to 2 more tablespoons, 1 tablespoon at a time, if needed, to reach desired consistency.)
Turn the dough out on a lightly floured work surface, and shape into a ball. Wrap in plastic wrap, and refrigerate at least 30 minutes or up to 2 days.