Add the rolled oats, pumpkin puree, ground cinnamon, nutmeg, and ginger to a mixing bowl, and stir well to combine until the oats are evenly coated with the spices and pumpkin.
Pour in the milk and maple syrup, then fold everything together until the mixture is smooth and has a uniform consistency, with no dry oats remaining.
Add the vanilla extract if using, and give the mixture a quick stir to incorporate.
Transfer the mixture into a jar or airtight container, seal tightly, and place it in the refrigerator overnight or for at least 4 hours to allow the oats to soak and thicken.
In the morning, remove the oats from the fridge, give them a gentle stir, and check the consistency. If desired, add extra milk to loosen or a sprinkle of cinnamon for additional flavor.
Spoon the chilled pumpkin spice oats into bowls, and enjoy the rich, creamy texture and warm aromatic spices with your favorite toppings if desired.