To prepare the crust, put the butter and sugar in the bowl of a heavy-duty mixer and mix on medium speed until smooth and creamy. Add the yolks one at a time, mixing well after each addition. Add the sour cream and mix well. Add the flour, baking powder, baking soda, vanilla, and ginger and mix well. Set aside.
To prepare the filling, preheat the oven to 375 degrees. Butter a 2-quart baking dish or eight 8-ounce individual gratin cups. Put the berries, sugar, cinnamon, ginger, lemon, cornstarch, and butter in a large bowl and toss to mix. Pour the filling into the baking dish, or divide among the gratin cups, and top with the crust, gently spreading the dough to cover the filling. Bake in the oven until the topping is golden brown and a knife inserted in the center comes out clean, about 40 minutes. Remove from oven and cool for 10 minutes.
Spoon the warm cobbler into individual serving bowls. Top with a scoop of ice cream, garnish with several mint leaves, and serve.
Per serving: 448 Calories (kcal); 20g Total Fat; (38% calories from fat); 4g Protein; 66g Carbohydrate; 125mg Cholesterol; 99mg Sodium Food Exchanges: 1 1/2 Grain(Starch); 0 Lean Meat; 0 Vegetable; 0 Fruit; 4 Fat; 3 Other Carbohydrates