Start by heating your oven to 375°F so it's fully ready when your batter is. While it warms up, lightly grease your baking dish with butter or a light coating of oil spray. This little step keeps the edges from sticking and makes cleanup so much easier later.
In your large bowl, add the rolled oats, pumpkin pie spice, baking powder, and salt. Give everything a good stir so the spice and baking powder are evenly distributed. I like to do this first so I'm not chasing clumps of spice once the wet ingredients go in.
Add the pumpkin puree, milk, eggs, vanilla, and maple syrup right into the same bowl with the oats. Whisk it all together until you don't see any streaks of egg or pumpkin left. The batter will look thick and speckled with spice, which is exactly what you want.
Pour the mixture into your prepared baking dish and use a spatula to spread it into an even layer. If you're using pecans or walnuts, scatter them across the top now so they toast up nicely in the oven.
Slide the dish into the oven and bake for 30 to 35 minutes. You'll know it's ready when the edges are puffed and golden and the center feels set rather than jiggly. A toothpick inserted in the middle should come out clean.
Let the baked oatmeal rest for about 5 to 10 minutes before slicing. This little pause lets it firm up so your pieces hold together instead of falling apart when you serve them.