Add oil, applesauce, yogurt, and both sugars in a second large bowl. Mix well to combine.
Add in the eggs and vanilla beating as they are added in with the oil, applesauce, and sugar mixture.
Slowly add the wet mixture in with the dry ingredients.
Stir slightly to just incorporate. (Do not over mix)
Add chopped apples to the batter. Use a spatula to fold in gently.
Scoop the batter into the prepped fluted cake pan.
Bake at 325 degrees for 55-65 minutes. (Check by inserting a l wooden toothpick into center. If it comes out clean the cake is done.) (Watch the cake to make sure that the edges of the cake don't brown you may have to cover it with foil.)