In a large bowl, whisk together the eggs, brown sugar, applesauce, milk, coconut oil, and vanilla. Sprinkle the baking powder, cinnamon, and salt on top and whisk until smooth. Add the oats, cranberries, and walnuts and mix with a spatula to combine.

Set the mixture aside for 20 minutes to hydrate the oats. Meanwhile, preheat the oven to 350°F and grease an 8x8-inch square baking dish. Line the bottom and two sides with a sheet of parchment paper.

Spread the oat mixture evenly in the prepared pan. Bake for 32 to 37 minutes, or until the middle is set.

Allow to cool completely in the pan before slicing and serving.

Store cooled bars in an airtight container in the refrigerator for up to 4 days.