Preheat oven to 350°F (175°C). Lightly grease a 9-inch (23cm) square baking pan or line with parchment paper.
Mix dry ingredients: In a large bowl, whisk together the oats, whole wheat flour, baking powder, baking soda, cinnamon, nutmeg, and salt.
Mix wet ingredients: In a separate bowl, whisk the egg whites, melted coconut oil, and vanilla extract until smooth. Add the Greek yogurt, maple syrup, and milk, then whisk until fully combined.
Combine: Pour the wet ingredients into the dry ingredients and mix just until combined. Fold in the diced apples. Do not overmix.
Transfer the batter to the prepared pan and spread evenly.
Bake: Bake for 25–30 minutes, or until lightly golden and a toothpick inserted into the center comes out clean.
Let cool for at least 15 minutes before slicing into squares or bars.
Video
Notes
Oats: Quick oats work best for a soft, tender texture. You can use rolled oats, but the cake will have a heartier texture. Do not use steel-cut oats.
Flour: Whole wheat flour gives the cake a wholesome flavor and extra fiber. For a lighter texture, replace half the flour with all-purpose flour. To make the recipe gluten-free, use certified gluten-free oats and a 1:1 gluten-free flour blend.
Sweetness: This is a lightly sweetened snack cake. For a sweeter cake, increase the maple syrup slightly or add a handful of chocolate chips or raisins.
Storage: Store covered at room temperature for 1 day or in the refrigerator for up to 5 days. The bars also freeze well for up to 2 months.