Preheat the oven to 350°F and lightly grease a round cake pan.
In a bowl, whisk together flour, cocoa powder, baking powder, baking soda, and salt.
In another bowl, beat eggs with sugar substitute until smooth. Add applesauce, yogurt, milk, and vanilla. Mix well.
Gradually fold the dry ingredients into the wet mixture until just combined.
Pour the batter into the prepared pan and spread evenly.
Bake for 25 to 30 minutes until a toothpick inserted comes out clean.
Let the cake cool before slicing and serving.