Stir together apples, ⅔ cup sugar and 4 Tbsp water in a large saucepan. Simmer, covered for 5 minutes or until fruit is tender.
Add 2 Tbsp water and 1 Tbsp cornstarch. Cook, stirring, until thick and bubbly.
In a medium bowl stir together flour, 2 Tbsp sugar, and baking powder.
Cut in butter until mixture resembles large crumbs. Set aside.
In a small bowl stir together the egg and milk. Add to flour mixture, just to moisten.
Transfer filling to 2-quart square baking dish.
Using a large spoon, drop topping into small mounds on top of the filling.
Bake for 20–25 minutes in a 400 °F (205 °C) oven.