Preheat the oven to 375ºF. Add the applesauce, eggs, brown sugar, vanilla, cinnamon, salt, and baking powder to a large bowl and whisk together until smooth. Add the milk and whisk until smooth again.
Slice the cranberries in half (no need to thaw if frozen) and add them to the bowl of wet ingredients along with the rolled oats. Stir until everything is evenly combined.
Pour the oat mixture into a 2-quart casserole dish. Bake the oatmeal in the preheated oven for 45 minutes, or until the surface is a light golden brown and it is no longer sticky in the center. Serve hot or refrigerate until ready to eat.
*We used cranberries that had been previously frozen, but you can use fresh as well.**Make sure to get old-fashioned rolled oats instead of quick oats because they have a lot more texture and will keep your baked oatmeal from being too mushy