Preheat your oven to 350°F (175°C). Line a 9x5 inch loaf pan with parchment paper and lightly grease it.
In a large mixing bowl, whisk together the oil, granulated sugar, and brown sugar until smooth.
Add the large eggs to the mixture and whisk until fully incorporated.
Add the unsweetened applesauce, vanilla extract, and Greek yogurt, mixing until well combined.
In a separate bowl, whisk together the all-purpose flour, whole wheat flour, baking soda, baking powder, ground cinnamon, ground nutmeg, and optional salt. Gently stir this into the wet ingredients.
Pour the batter into the prepared loaf pan and spread evenly.
Bake for 45-55 minutes or until a toothpick inserted comes out with moist crumbs.
Allow to cool for 10 minutes in the pan before transferring to a wire rack to cool completely.