Roll out pastry dough into a 9-10 inch circle. Transfer to a parchment lined sheet pan. Preheat oven to 400F and position rack in the lower 1/3 of the oven.
In a bowl, combine the sugar and cornstarch and then mix in the fruit and basil. Let mixture sit for 15 minutes to allow juices to come out and then remix before you place onto galette crust.
Lay fruit mixture onto the crust leaving 2 inch border around the edges. Fold the uncovered edges over the apples creating pleats as you go along. Wet crust with a bit of water and sprinkle with sugar.
Bake for 35-40 minutes or until crust is golden brown and crisp (fruit mixture should be bubbling). Remove from oven, transfer to a cooling rack and cool for 10 minutes. Cut using a sharp knife into wedges and serve.
Plain Short Pastry
Combine flour, salt & sugar. Work in butter until mixture is crumbly. Gradually add lemon juice and water, mixing just until the dough begins to come together.
Turn out onto a floured work surface, gather dough together and shape into a disk, and wrap in plastic- Rest in the refrigerator 30 minutes before rolling out.
You can make this dough very easily in a food processor or by hand.