What is the correct procedure for making espresso in a stovetop espresso maker?

Follow the instructions that came with the esspresso maker.

If you have the kind that I have (this kind), you put water in the bottom, espresso grounds in the middle, and put it on the stove. The steam from the water percolates up through the coffee, and boils out the top pipe, into the top compartment. When it stops bubbling through, or when you have enough espresso, you take it off the heat and pour out the espresso from the top. You have to essentially boil it, because how else would the water get from the bottom to the top, except in the form of steam?

The essential brewing characteristics of espresso, as I understand it, are that it’s brewed under high heat and pressure. You can see why steam-brewing it would provide both conditions.

Ditto what hannahsugs said, make sure to keep the handle away from the heat (easy to forget) and use med-hi setting so you don’t burn the coffee. Also, the coffee will only be as good as the job you do packing it into the reservoir. Don’t overdo it, but it should be tamped down for the best flavor.

One point that hasn’t been mentioned is that the coffee should be ground finer than you would for drip or French press.

@Kevbo ~ excellent point. Personally, I use Cuban coffee like Pilon or Bustelo. My fave is Lavazza though!

Thank you all very much! Just made one to specs and it was delicious.

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