Preheat the oven to 375 degrees and grease an 8x8 inch baking dish with butter or oil.
In a large bowl, mix the egg, applesauce, milk, maple syrup, and vanilla extract.
In a separate bowl, stir together the oats, walnuts, and salt.
Add the dry ingredients to the wet ingredients and stir until combined.
Stir in the berries.
Transfer the mixture to the baking dish and bake for 30 minutes, or until the oatmeal is set and no longer liquidy. Cool slightly, then cut it into four pieces to serve.