In a large mixing bowl, combine oats, sugar, baking powder, cinnamon, and salt.

In a separate large mixing bowl, whisk together eggs, milk, applesauce, and vanilla extract. Add dry ingredients to wet ingredients and mix until combined. Set aside for at least 20 minutes to set.

Meanwhile, preheat oven to 350 degrees F and line an 8x8 or 6x9 casserole dish with parchment paper.

Pour oatmeal mixture into prepared casserole dish and bake for 30-35 minutes, or until edges are golden brown. Cool at least 5 minutes before slicing.