Preheat oven to 350 degrees.
In a large mixing bowl, stir together the oats, cinnamon, baking powder, sea salt, apples, and half of the walnuts.
In a small mixing bowl, whisk the eggs, then add honey, milk and vanilla, whisking thoroughly. (The honey may clump a little when the cold milk is added. Just whisk the best you can, and it'll turn out fine.)
Add the wet ingredients to the dry and stir to mix.
Pour the mixture into a 8x8 square pan. Sprinkle with remaining walnuts, then drizzle the melted butter evenly over the top.
Bake for 30-35 minutes, or until top is deep brown and bubbly. (Don't overcook! Remove and test doneness with a spoon if needed the baked oatmeal should be very moist, yet have some form. It will continue to set as it cools.)
While oatmeal is in the oven, whisk icing ingredients together. Drizzle over hot oatmeal. (I like to reserve about half the icing for drizzling additional over each bowl when served.)