Whisk together the flour, baking powder, salt and 1 cup granulated sugar in a bowl. Stir in the half-and-half, mixing just until combined.
Add the butter to a 9-by-13-inch baking dish, tilting to coat evenly. Pour the batter over the butter in the baking dish, then set aside.
Bring the berries, brown sugar, lemon juice, cinnamon, nutmeg, apples, 2 tablespoons water and the remaining 1/2 cup granulated sugar to a boil. Cook for 2 minutes more. Pour the fruit and syrup over the batter in the baking dish without disturbing the batter layer.
Bake until golden brown and puffed on top, 45 to 50 minutes. Let cool slightly before serving.