Pre-heat oven to 375 degrees.
In a medium bowl, combine blueberries, sugar, basil and cornstarch. Set aside.
Stretch (or roll if you made your own) your pie crust on lightly floured parchment paper.
Place berries in the center of the crust. Make sure to leave about 2 inches boarder around the outside to fold over.
Fold the crust edges up and over the blueberries (I tucked as I circled the fruit).
Transfer the parchment to a baking sheet. Beat egg with water. Brush dough with egg wash and sprinkle evenly with sugar.
Bake for 35-40 minutes. Top the galette with crumbled goat cheese and bake for an additional 10-15 minutes or until the fruit center is bubbly and the crust is golden brown. Remove from oven and top with chopped fresh basil.
Allow galette to rest at least 15 minutes before slicing.