Prepare the coffee and pour it into a large mug or glass mason jar. Add pumpkin puree, maple syrup, pumpkin pie spice, and vanilla and stir until well combined.
Prepare the oatmeal: Combine the water, apple juice, and apples in a saucepan. Bring to a boil over high heat, and stir in the rolled oats and cinnamon. Return to a boil, then reduce heat to low, and simmer until thick, about 3 minutes.
Prepare the latte: Pour milk into a small pot and heat over medium-low heat until it is hot and almost simmering, but do not boil the milk.
Use a milk frother or a whisk to froth your milk until foamy, then pour into the mug on top of the pumpkin-coffee mixture. Reserve the extra foam, and spoon it on top.
Portion the oatmeal into bowls, and pour milk over the top. Serve with the latte, topped with whipped cream and a sprinkle of pumpkin spice.