Preheat the oven to 200°F. Line a sheet pan with parchment paper.
Put the egg whites into the bowl of a stand mixer fitted with the whisk attachment, or a large bowl if using a hand mixer, and whisk until white and frothy and almost beginning to hold soft peaks, about 5 minutes.
Keep whisking while slowly adding the espresso powder and then the sugar, little by little. When everything has been combined, whisk the mixture until the meringue holds stiff peaks, about 5 more minutes. Do not overbeat.
Use a spoon to make large dollops of meringue on the prepared sheet pan; you should end up with 8 individual meringues, evenly spaced. Bake the meringues for 45 minutes, then turn off the heat and let them cool in the oven. When the meringues have cooled, remove them from the pan with a spatula. Store the meringues in an airtight container for 2 to 3 days.