Preheat the oven to 350F and grease an 8X8 glass baking dish.
In a medium bowl, combine the oats, sugar, brown sugar, baking powder, pumpkin spice, and salt. Mix well.
Add in the milk, eggs, pumpkin puree, and vanilla extract. Fold in with a silicone spatula until well combined.
Add in the melted and cooled butter, mixing thoroughly.
Pour the oatmeal mixture into the prepared baking dish and bake in the oven for 40-45 minutes.
Allow to cool for 5-10 minutes before slicing and serving with milk or whipped cream.