Preheat your oven to 375℉ (190℃). Lightly grease an 8×8 inch baking dish with oil, making sure to coat all sides to prevent sticking.
In a medium bowl, combine the old-fashioned oats, pumpkin pie spice blend, baking powder, and salt. Stir them together until well mixed, making sure the spices and leavening are evenly distributed.
Add the pumpkin puree, milk, eggs (or flaxseed eggs for a vegan option), pure vanilla extract, and maple syrup or honey to the bowl with the dry ingredients. Stir until everything is fully combined and the batter is smooth. If you like, you can also fold in chocolate chips, chopped nuts, raisins, or your favorite toppings at this time.
Spread the oatmeal mixture evenly into the prepared baking dish (from Step 1). Bake in the preheated oven for 30-35 minutes, or until the edges are puffed up, the center is set, and the top is golden. I like to bake it until the edges look slightly crisp for extra texture.
Allow the baked oatmeal to cool in the pan for about 5 minutes before slicing. It will be soft at first but will firm up as it cools. Enjoy it warm, optionally topped with yogurt, a splash of milk, a drizzle of honey or maple syrup, fruit, or whipped cream—or just savor it plain. Let the leftovers cool completely before storing them in an airtight container in the fridge for up to 4 days. Personally, a little splash of milk when reheating makes it extra creamy.