In a large bowl combine all of the baked oatmeal ingredients, except for the oats and whisk until thoroughly combined.
Stir in the oats and then pour the mixture into a greased 8x8 baking dish.
Bake at 350 for about 25 minutes, or just until firm in the middle.
To make the caramel vanilla icing:
Process the coconut sugar ½ cup at a time in a coffee grinder until powdered.
In a bowl combine the powdered coconut sugar, butter and vanilla and mix thoroughly. I use the whisk attachment on my mixer. Add milk a small drizzle at a time until the icing is the desired consistency.
Allow the baked oatmeal to cool a little before spreading the icing on top.