Combine first 3 ingredients in a bowl. Cover and let apples stand 30 minutes; stirring once.
Whisk together the flour, baking powder, cinnamon and salt in a second bowl. Stir in nuts. Combine milk, oil, egg and vanilla in a third, smaller bowl.
Coat an 8” square baking pan with vegetable oil spray. Cut an 8” by 12” piece of parchment paper to fit the bottom and up 2 of the 4 sides of the pan. (The parchment extending the sides of the pan will later be used as handles to lift the cake out once baked.) When the apples have sat 30 minutes, preheat the oven to 350 degrees F.
Pour the egg/oil mixture over the apples and mix to combine. Add flour mixture and stir until a batter forms. Spoon batter into the pan.
Bake 40 minutes, or until the cake springs back when touched in the very centre. Cool the cake on a rack. Cut around the edges of the cake to loosen from the pan. Grab on to the parchment and lift cake out of pan. Dust with icing sugar if desired. Cut into squares and serve.