Preheat oven to 350°. Grease/spray a 13"x9" baking dish.
Beat eggs in a large mixing bowl.
Add sugar, applesauce & oil and beat.
Stir in flour, baking soda, cinnamon, nutmeg, salt & vanilla until combined.
Stir in apples.
Pour batter into baking dish. Bake for 30 - 36 minutes. Top will be golden brown and toothpick inserted near center should come out clean.
Cool on wire rack & glaze.
Combine butter, brown sugar, heavy cream & vanilla in a small saucepan over medium heat.
Stirring often, bring to a light boil.
Stirring constantly, let boil for a minute for a thin glaze and 2-3 minutes for a thicker glaze.
Let cool for a few minutes & pour/spoon glaze over cake and spread evenly with a spoon or spatula.
Serve & enjoy. Store cake loosely covered.