Preheat oven to 350°F.Butter a 2 ½ quart baking dish.Combine all dry ingredients.Place half the oat mixture in the baking dish, top with half the berries, and then top with the remaining oat mixture.Whisk the eggs, milk, vanilla, and melted butter. Pour over the oats.Top the oats with the remaining berries.Gently shake the baking dish back and forth from side to side to allow the wet mixture to get down into the oats.Bake uncovered for about 40 minutes, until oats are tender, and the mixture is set.Serve immediately with a splash of milk, or cool, then cover and refrigerate to reheat later.