Combine the water, butter, and salt in a medium-sized saucepan. Heat until the butter has melted, and bring to a boil.
Remove the pan from the heat, and add the flour all at once, stirring vigorously.
Return the pan to the burner and cook over medium heat, continue stirring continually, until the mixture smooths out and follows the spoon around the pan; should happen quickly.
Remove from the heat. Allow the mixture cool for 10 minutes. Test by placing your finger in for a few seconds. It's ready if you can
Transfer mixture to a mixer, and beat in the eggs one at a time. At first it may look curdled but when you add the last egg it should become smooth. Beat for at least 2 minutes after adding the last egg.
Using a medium cookie scoop tp drop the batter onto the prepared baking sheets. Space the dough about 2" apart, to allow for expansion.
Bake the pastries for 13 minutes. Reduce the oven temperature to 350°F and bake for an additional 8-10 minutes, until pastries are a medium golden brown. Don't open the oven door while the pastries are baking.
Remove the pastries from the oven. Turn off the oven. Make a small slit in the side of each, and return them to the oven for about 5-10 minutes allowing the steam to escape. Place them on a rack to cool. When they are cool, split each in half to make top and bottom pieces. Splitting these allows them to be exposed to the air and keeps them from being soggy.