Preheat oven to 350 degrees. Butter 10-inch(26 cm) springform pan (with a removable base).
Separate the egg yolks from the whites. In a medium bowl mix egg yolks with 1/3 cup sugar until thick, creamy and pale yellow colored. Add butter and mix then add the cold water, vanilla extract, cinnamon and lemon zest and mix well.
Whip egg whites until foamy with a mixer. Gradually add the 1/3 cup sugar left whipping the whole time until it holds very stiff peaks. Add the whites to the yolks mixture.
Gently fold in the flour and baking powder.
Peel the apples and sprinkle with fresh lemon juice. Cut 2 of the apples in small pieces and 1 apple in thin slices for the top of the cake.
Incorporate the apple small pieces into the batter. Pour the mixture into the prepared pan. Arrange the apple slices on top and add the walnuts.
Bake for about 40 50 minutes until a toothpick inserted in the center of the cake comes out clean.
Serve along a good cup of coffee or tea.