Preheat oven to 350ºF (175ºC). Prepare a 9-inch pie pan by greasing well with butter.
Combine apricots, sugar, cornstarch and grated ginger. Arrange in an even layer in the pie pan.
In a food processor, blitz butter, sugar, flour, baking powder, and salt until the butter is broken up into pea-sized pieces. Add soy milk and grated ginger and blitz until dough forms. Tear into pieces and arrange on top in a cobbler-like pattern. Sprinkle with sugar, and bake for 50 minutes.
The juices from the fruit may bubble over, so put a baking tray underneath to catch the juices.
Remove from oven once the edges of the top of the cobbler have become golden brown. Let cool on a wire rack, and serve once just warm.