Preheat the oven to 180°C (350°F).
In a deep bowl, beat the eggs with the vanilla and fructose sugar using an electric mixer on high speed for about 3 minutes. Gradually pour in the oil and yogurt while mixing continuously.
In another bowl, mix the whole wheat flour, baking powder, baking soda, salt, cinnamon, and brown sugar until well combined.
Add the flour mixture to the egg mixture and mix well until you get a smooth cake batter.
Pour the cake batter into a greased baking pan. Arrange the apple slices evenly on top.
Bake the cake in the oven for 35-40 minutes, or until fully cooked.
Remove the apple cake from the oven and let it cool. Slice it and serve with a cup of tea.