Warm the milk in a saucepan over medium heat until it begins to steam, but don't let it boil. Whisk in the pumpkin puree until the mixture is silky and evenly combined.
Stir in the rolled oats along with the pumpkin pie spice, cinnamon, and salt. Cook over medium-low heat, stirring every minute to keep the oats from sticking to the bottom of the pan.
Once the oats begin to soften, mix in the maple syrup and vanilla extract. Continue cooking until the oatmeal is thick, creamy, and the oats are fully tender.
Taste the oatmeal and adjust the sweetness or spices if needed. If it's too thick, loosen it with an extra splash of milk until it reaches your preferred consistency.
Spoon the oatmeal into serving bowls and add your favorite toppings such as toasted pecans, pumpkin seeds, sliced bananas, diced apples, or an extra drizzle of maple syrup. Serve immediately while warm.