In a small saucepan over medium heat, whisk together the pumpkin puree, sugar or sweetener, pumpkin pie spice, cinnamon, nutmeg, vanilla extract, and milk until hot and well combined. Do not let it boil.
Add the brewed espresso or strong coffee and stir until smooth and steaming.
For a hot latte, pour into a mug and top with whipped cream and a light dusting of pumpkin pie spice if desired.
For an iced latte, let the latte mixture cool slightly, then fill a glass with ice and pour the cooled mixture over the ice.
Top with whipped cream and a sprinkle of pumpkin pie spice, if using, and serve immediately.
Notes
For a smoother latte, whisk the pumpkin puree well while heating to fully dissolve it into the milk. Use any milk you like, and adjust the sweetener and spice level to taste.