Preheat your oven to 350°F while you get everything else ready. Lightly coat your 9x9-inch baking pan with cooking spray or a thin layer of oil so nothing sticks once it's baked. Set the pan aside while you mix your ingredients.
In a large mixing bowl, combine the oats, baking powder, cinnamon, and salt. Give everything a good stir so the leavening and spices are evenly distributed throughout the oats before you add anything wet.
In a separate smaller bowl, beat the egg first until it's smooth. Then whisk in the milk, pumpkin puree, maple syrup, and vanilla extract until the mixture looks fully combined and slightly creamy.
Pour the wet mixture over your bowl of dry oats and stir until every oat is coated and no dry streaks remain. Gently fold in the chocolate chips last, so they stay whole instead of breaking apart from too much stirring.
Pour the finished batter into your prepared pan and spread it evenly with a spatula. Bake for about 30 minutes, until the top looks set and turns a light golden color, and a knife inserted in the center comes out clean.
Let the baked oatmeal rest for about 5 minutes before cutting into it. This short resting time helps it firm up just enough to slice into neat squares instead of falling apart.