Preheat the oven to 325°F. Butter a 10-inch deep pie plate or a shallow baking dish.
Arrange the blueberries and ginger in the bottom of the buttered pie plate and sprinkle with 1/4 cup of the sugar.
Pour the milk into the blender and add the eggs, flour, vanilla, and the remaining tablespoon of sugar. Blend on high speed until mixed, about 1 minute.
Pour the batter directly from the blender over the fruit in the pan. Bake for 25 to 30 minutes, or until the clafouti is lightly browned on the edges. Top with shaved chocolate curls. Cut into six pie-shaped wedges and serve while still warm.