Set the pan over medium low heat and cook for 2 to 3 minutes, whisking often, until the paste bubbles gently, darkens a shade, and smells warm and toasty.

Pour in the remaining 1 3/4 cups milk and heat for 4 to 5 minutes, whisking every minute, until the milk reaches 150 to 160°F, steam rises, and tiny bubbles ring the edge of the pan.

Take the pan off the heat and stir in the vanilla. Whisk hard for 10 seconds until the milk looks pale orange and completely smooth.

Froth the milk for 30 to 45 seconds with a handheld frother, or whisk fast in a figure eight for 45 seconds, until the top looks creamy and thick with about 1/2 inch of tiny bubbles.

Divide the hot espresso between two warmed mugs, about 1/4 cup in each, so the coffee forms a dark layer about 1 inch deep.

Hold the foam back with a spoon and pour the pumpkin milk into the mugs, then spoon the foam on top. Add whipped cream and a dusting of pumpkin pie spice if you like. Each mug should be full to about 1/2 inch below the rim.