Cake Mixture: Whisk eggs and egg white until fluffy in a bowl. Stir in the sugar and vanilla. Fold in the flour and baking powder with a scraper. Then add the oil and stir in with the scraper also, the mixture may appear very oily.
Line a baking tray with baking paper and sprinkle with cinnamon then pour the mixture on the baking tray and spread evenly.
Peel, core and cut the apples into quarters or eighths, depending on size. Drizzle with lemon juice.
Lay the apple slices into the cake mixture with the curved side up.
Preheat the oven to 180 degrees C.
Streusel: Finely chop the cold butter then mix with the sugar, vanilla and egg yolks with a dough hook (or combine by hand). Sift the flour and baking soda then combine until looks like crumbs.
Sprinkle the crumbs over the apple mixture then bake in the preheated oven for about 45 minutes Immediately after removing from the oven sprinkle melted butter over the slice.