Pour the water or milk into a saucepan and bring it to a gentle simmer over medium heat.
Add the rolled oats to the simmering liquid, stirring occasionally to prevent sticking.
Cook the oats, stirring often, until they begin to soften and absorb the liquid, about 3-4 minutes.
Stir in the pumpkin puree, cinnamon, and nutmeg, mixing thoroughly to combine all the flavors evenly.
Reduce the heat to low and continue to cook, stirring frequently, until the oatmeal thickens to a creamy consistency, about 3-4 minutes.
Remove from heat and stir in maple syrup if desired for added sweetness and flavor.
Pour the hot pumpkin oatmeal into bowls, and optionally add toppings like nuts or seeds for extra texture.
Enjoy immediately, noting the thick, creamy texture and warm spiced aroma that fills the kitchen.