BEFORE BAKING: Grease a baking tray with butter and dust with flour or fine breadcrumbs. Preheat the oven to 340 °F (170 °C).
Place the softened butter in a bowl, add the coarse sugar, and beat them together with a hand spatula. Then incorporate the egg yolks, one at a time. Finally, add the flour mixed with baking powder and milk. Work into a soft, smooth dough.
Separate a third of the dough, wrap it in plastic, and place it in the freezer to stiffen up.
Press the remaining dough into a thin layer on the bottom of the prepared baking sheet.
Chop the walnuts coarsely using a large knife.
Peel the apples, remove the cores and slice them thinly. You can also grate them coarsely. Sprinkle with lemon juice to prevent the apples from browning.
Spread the apples evenly over the dough, dust with cinnamon, about two tablespoons of sugar, and chopped nuts.
Beat the egg whites using a hand-held electric mixer with the remaining sugar until stiff. Finally, whisk in a tablespoon of wine vinegar. Carefully spread the snow over the apple layer.
Take the remaining third of the dough out of the freezer and grate it coarsely. Sprinkle the grated dough over the meringue layer. The dough should not form a thick impenetrable layer; instead, the meringue should be visible under the batter.
Bake the cake for 45 minutes in an oven preheated to 340 °F (170 °C).