Preheat the oven to 375ºF. In a large bowl, whisk together the pumpkin purée, brown sugar, eggs, vanilla, pumpkin pie spice, salt, and baking powder until smooth.
Add the milk and whisk until smooth again.
Stir the dry oats into the pumpkin mixture.
Pour the oats into an 8x8-inch baking dish.
Bake the oats in the preheated oven for 45 minutes, or until the center no longer looks wet and the edges are lightly golden brown.
Serve hot right out of the oven or refrigerate until ready to serve. The baked oats can be eaten cold or reheated. Top with milk, maple syrup, whipped cream, or nuts if desired.