Place the canned pumpkin, pumpkin spice, cinnamon powder, and black pepper in a small saucepan over medium heat and cook for 2 minutes, stirring constantly. It get really hot and start smelling really good.
Add the sugar and continue to stir the mixture until it starts to darken slightly in color and thicken.
Start whisking the pumpkin mix as you slowly add in the milk and the vanilla extract. Let it warm over medium heat, and keep an eye on it to make sure it doesn't boil over.
Once it starts boiling, turn the stove off, use an immersion stick blender, a traditional blender, or a handheld mixer to beat until it's completely blended and frothy. If you're using a traditional blender, be sure to use a hand towel to hold the lid down tight.
Place 3 tablespoons of espresso in each mug, add the frothy pumpkin milk on top, and top with whipped cream. Sprinkle with a pinch of nutmeg. Serve immediately.