Optional garnish: sliced almonds and demerara or turbinado sugar
Place rack in lower third of oven and preheat oven to 400ºF. Coat 9-by-13-inch baking dish with cooking spray and set aside.
In large bowl, combine 2 cups of all-purpose flour and whole wheat flour. Add granulated sugar, baking powder and salt and stir to combine.
Cut butter into dry ingredients until mixture resembles coarse meal.
In another small bowl, whisk egg until combined. Whisk in 1/2 cup buttermilk or milk and lemon juice. Stir egg-milk mixture into dry ingredients just until soft dough is formed, adding additional milk if needed.
In large bowl, toss together apples, brown sugar, lemon zest, cornstarch and remaining 1/4 cup all-purpose flour. Spread apple mixture in prepared dish and top with cheese.
Drop dough in large mounds on top of apples, spreading to edges. Sprinkle with toasted almonds and demerara or turbinado sugar if desired.
Bake in lower third of oven for 40 to 50 minutes or until topping is golden brown and apples are bubbling and tender when pierced with knife (cover topping loosely with sheet of foil if browning too quickly).