In a medium saucepan over medium-high heat, combine 1 cup water, the butter and salt. Heat until the butter has melted and the water is boiling.
Add the flour and cook, stirring constantly with a wooden spoon, until the mixture thickens up and begins to create a dough ball in the center of the pan and the dough is completely pulling away from the sides of the pan, about 2 minutes.
Transfer the dough to a mixing bowl or the bowl of a stand mixer fitted with the paddle attachment. On low speed, add the eggs one at a time, scraping the bowl well after each addition and beating until the bowl feels cool (the mixture should be very smooth and silky).
Transfer the dough to a re-sealable plastic bag and cut about 1/2-inch off one corner. Using this as a piping bag, pipe the mixture into the desired shapes on a parchment-lined baking sheet. Bake until golden brown and puffed, about 40 minutes.
Cook's Note: These pastries can be made a day or two ahead of time and kept in an airtight container at room temperature. If they feel soggy when you take them out, pop them into a 400 degree F oven for a couple of minutes until they crisp up again. Allow them to cool before filling.