Preheat your oven to 350°F (175°C). Line an 8 x 8-inch baking pan with parchment paper, leaving extra paper hanging over the sides.
Cut small slits in each corner so the paper fits neatly inside the pan. This makes removing the bars much easier after baking.
Add 2 cups old-fashioned rolled oats, 1/2 cup cane sugar, 1 1/2 teaspoons baking powder, 1/2 teaspoon ground cinnamon, and 1/2 teaspoon salt to a large mixing bowl.
Whisk everything together until the ingredients are evenly combined. This helps distribute the cinnamon and baking powder throughout the batter.
In a separate bowl or large measuring cup, whisk together 2 large eggs, 1/2 cup almond milk, 1/4 cup unsweetened applesauce, and 1 teaspoon vanilla extract until smooth. The mixture should look well blended with no streaks of egg remaining.
Pour the wet ingredients into the bowl of dry ingredients. Stir gently with a rubber spatula or wooden spoon until every oat is coated. Stop mixing as soon as no dry spots remain to keep the bars soft after baking.
Leave the batter at room temperature for 20 minutes before adding the mix-ins. During this time, the oats absorb the liquid and become softer. This simple step helps the bars hold together well after they are baked and sliced.
Add 1/4 cup finely chopped walnuts and 1/4 cup dried cranberries to the rested batter. Fold them in gently until they are evenly distributed. Every scoop of batter should contain a little of each ingredient.
Transfer the batter to the prepared baking pan. Use a spatula to spread it evenly into all four corners. Smooth the top so the bars bake evenly and have a uniform thickness from edge to edge.
Place the pan on the center oven rack and bake for 30 to 35 minutes. The top should turn lightly golden, and the center should feel set when touched gently. Avoid overbaking, as this can dry out the bars.
Set the pan on a wire rack and allow the bars to cool completely. Once cooled, lift the entire batch from the pan using the parchment paper. Cooling first helps the bars stay firm and prevents them from breaking.
Place the cooled bars on a cutting board and use a sharp knife to cut them into 16 even squares. Serve right away or save them for breakfast or a quick snack during the week.