Preheat your oven to 350°F (175°C). Line an 8-inch square pan with parchment paper, making sure to leave some overhang on the edges for easy removal later.
In a medium bowl, combine your dry ingredients: rolled oats, sugar, baking powder, salt, and cinnamon. Stir them together until they are well mixed.
In a separate large bowl, mix the wet ingredients: eggs, milk, applesauce, and vanilla extract. Whisk together until everything is well combined.
Transfer the dry mixture into the bowl with the wet ingredients. Stir until everything is just combined. Let the mixture sit for about 20 minutes.
Gently fold in the walnuts and cranberries into the mixture. Spread the mixture evenly into the prepared 8-inch square pan.
Bake in the preheated oven for 30-35 minutes or until the edges are golden brown and a toothpick inserted into the center comes out clean. Allow the bars to cool in the pan for about 5 minutes.
Using the parchment overhang, lift the baked mixture out of the pan and transfer it to a cutting board. Slice into 16 bars.
