Special equipment: a piping bag with a 1/2-inch plain tip
For the dough: Preheat the oven to 400 degrees F. Line two baking sheets with parchment paper.
Combine the butter, granulated sugar, salt and water in a medium saucepan. Bring to a boil and remove from the heat. Add the flour, then return to the heat, mixing vigorously with a wooden spoon until all the flour is incorporated and the mixture forms a ball.
Transfer the dough to the bowl of a stand mixer fitted with the paddle attachment and mix on the lowest speed until the dough cools and the steam dissipates, about 4 minutes. Add 4 eggs, one at a time, letting each egg become fully incorporated before adding the next. The dough should be shiny, stretchy and slowly fall from a spoon in thick ribbons. If necessary, beat the remaining egg in a small bowl and add a tablespoon at a time until the dough looks correct.
Transfer the dough to a piping bag fitted with a 1/2-inch plain tip. Pipe 2-inch mounds onto the prepared baking sheets, about 2 inches apart. Bake until the puffs are golden brown and sound hollow when tapped, about 25 minutes. Prick each puff with a skewer to allow the steam to escape, then remove the puffs to a rack to cool completely.
Use a serrated knife to carefully cut the tops off the puffs; reserve the tops.
For the cream: Microwave 2 tablespoons of the cream in a small bowl until warm. Add the espresso powder and stir until dissolved; place in the refrigerator to chill.
Put the remaining cream in a large bowl, along with the vanilla and 4 tablespoons of the confectioners' sugar. Beat with an electric mixer until the cream just holds stiff peaks.
Transfer half of the whipped cream to a piping bag fitted with a 1/2-inch plain or star tip. Pipe half of the puffs full of whipped cream; replace their tops.
Add the chilled coffee cream and the remaining 2 tablespoons confectioners' sugar to the remaining whipped cream in the bowl; beat until the cream returns to stiff peaks. Transfer to the piping bag (no need to clean in between) and fill the remaining puffs; replace the tops.
Dust the cream puffs with confectioners' sugar and serve immediately.