Preheat oven to 325, and lightly grease a fluted pan.
In a large bowl, mix together flour, baking soda, cinnamon, nutmeg and salt. Set aside.
In a separate large bowl, combine oil, applesauce, yogurt, and sugars. Mix together until well combined.
Beat in eggs and vanilla until creamy.
Pour mixture into dry ingredients and stir until just incorporated. Do not over mix here.
Fold in apple chunks.
Spoon mixture into prepared pan and bake for 55-65 minutes, or until wooden toothpick inserted into center comes out clean. It may be necessary to cover the edges of the cake with foil towards the end to avoid over browning.
For the Caramel Glaze
Melt butter over medium heat
Stir in brown sugar and cream and whisk together until fully mixed.
Bring mixture to a boil, stirring often.
Let boil for 1 minute with no stirring.
Reduce heat and let simmer 1 minute.
Remove from heat and let cool slightly to thicken (about 2 minutes)
Whisk in powdered sugar (sifted) and mix until smooth.
Immediately spoon glaze over cake and let cool before serving.
Notes
* I like to use Pink Lady and/or Honey Crisp apples, but use whatever your favorites are. A mixture of sweet and tart usually works well for apple desserts. ** If you do not sift the powdered sugar, it will be almost impossible to whisk out all of the little chunks--speaking from experience!