Preheat oven to 180 C / Gas 4. Grease an 20cm square baking dish with vegetable margarine.
Beat egg whites in a bowl with an electric mixer until stiff peaks form. Lift your beater or whisk straight up: the egg whites should form a sharp peak that holds its shape. Set aside.
Place the egg yolks, oil, and orange juice into a mixing bowl; beat with an electic mixer until creamy and thick, about 5 minutes. Stir in 200g sugar, mixing well, then lightly stir in the matzo meal and salt. Use a rubber spatula or wire whisk to fold about 1/3 of the beaten egg whites into the matzo meal mixture. Gently run the spatula through the centre of the mixture, then around the sides of the bowl, repeating until fully incorporated. Add the remaining egg whites, folding until just incorporated.
Mix together 150g sugar with cinnamon in a bowl. Spread half the batter into the prepared baking dish; distribute the apple quarters evenly over the batter. Sprinkle the apple pieces with about 1/2 of the sugar-cinnamon mixture, spread the remaining batter over the apples; sprinkle the remaining sugar-cinnamon mixture over the top of the cake.
Bake in the preheated oven until the cake is golden brown, about 45 minutes. Cut into squares while still warm.