With the rack in the middle position, preheat the oven to 190 °C (375 °F).
Combine the sugar and cornstarch in a square 20-cm (8-inch) baking pan or 2 litre (8 cup) soufflé dish. Add the fruit and ginger and toss well using a spatula. Place the pan on a baking sheet. Set aside.
In a food processor, combine the flour, sugar, baking powder, baking soda, and salt. Add the butter and pulse until it has the size of peas. Add the buttermilk and pulse until the dough is crumbly.
Scatter the dough over the fruit with your hands and bake for about 1 hour or until the pastry is golden brown and a toothpick inserted in the centre comes out clean. Serve warm or cold. If desired, serve with a scoop of vanilla ice cream.
Out of season, you can substitute the fresh peaches with 1.25 litres (5 cups) of canned peaches, well drained. In this case, reduce the sugar in the filling to 60 ml (¼ cup).
Recipes with the "Healthy Pick" stamp have been evaluated by a registered dietitian member of the Ordre professionnel des diététistes du Québec.