In a medium bowl, combine flour, brown sugar, and cinnamon. Cut in the cold butter with a pastry blender or your fingers until the mixture resembles coarse crumbs. Stir in chopped walnuts, if using. Set aside.

In a separate bowl, toss the sliced apples with granulated sugar and cinnamon. Set aside.

Preheat oven to 350°F (175°C). Grease and flour a 9x13 inch baking pan.

In a small bowl, whisk together flour, baking powder, baking soda, and salt.

In a large bowl, cream together softened butter and granulated sugar until light and fluffy.

Beat in the eggs one at a time, then stir in the vanilla extract.

Alternately add the dry ingredients and the buttermilk to the butter mixture, beginning and ending with the dry ingredients. Mix until just combined.

Spread half of the cake batter evenly into the prepared baking pan.

Layer the prepared apple filling over the batter.

Dollop the remaining cake batter over the apples, spreading gently to cover.

Sprinkle the crumble topping evenly over the cake batter.

Bake for 40-45 minutes, or until a wooden skewer inserted into the center comes out clean.

Let cool in the pan for at least 15 minutes before serving.