Preheat oven to 400°F. In a medium bowl, toss together blueberries, ¼ cup goat cheese, sugar, cornstarch, lemon juice, chopped basil and salt; set aside.
In a small bowl, beat together egg and 1 Tbp water; set aside.
Place pie crust on a parchment paper-lined baking sheet. Prick all over with fork. Leaving a 2-inch border, spoon the blueberry mixture into center of crust.
Fold the bare edges of pastry toward the center, over the filling. Pleat pastry as you go and leave center uncovered. Brush top of pastry with egg wash.
Bake for 20 to 25 minutes or until filling is just bubbling and pastry is golden. Sprinkle remaining goat cheese overfilling. Let cool for 10 to 15 minutes.
