Pour the water or milk into a medium saucepan and bring it to a gentle simmer over medium heat, causing a soft bubbling sound.
Add the rolled oats to the simmering liquid, stirring constantly to prevent sticking and clumping.
Cook the oats, stirring occasionally, until they start to soak up the liquid and become tender—about 5 minutes.
Stir in the roasted pumpkin puree, blending it evenly into the oats until fully incorporated and the mixture begins to thicken.
Add in the cinnamon, nutmeg, and a small pinch of salt, stirring to distribute the spices and enhance the aroma.
Reduce the heat to low and continue to cook the mixture for another 3-5 minutes, stirring frequently, until it reaches a creamy, velvety consistency.
Remove the saucepan from heat and let the oatmeal sit for a minute; it will slightly thicken as it cools.
Scoop the warm pumpkin spice oatmeal into bowls, garnishing with your favorite toppings like nuts, seeds, or a drizzle of maple syrup for added texture and sweetness.