Preheat your oven to 375°F. Line 2 large baking sheets with parchment paper, and set aside.
In a large saucepot, combine butter, water, sugar and salt. Place the pot over high heat and bring up to a boil.
Once boiling, remove from the heat and add in your cup of flour. Stir until you no longer see any dry flour and it starts to come together into a ball dough.
Return the pot to your stove burner (still set on medium heat). Cook the mixture, stirring constantly, for 1 to 2 minutes, or until your get a thin film of dough forming along the bottom of the pot (pictured above).
Transfer your dough to a heatproof mixing bowl. Set aside to cool slightly (about 5 to 10 minutes) before adding your eggs. Give your dough an occasional stir to make sure it's cooling evenly.
Crack your eggs into a bowl or measuring cup, and whisk to roughly break them up. Gradually add your eggs to the cooled dough (about 1/4 cup at a time), mixing well after each addition. It's normal for the mixture to separate as you add your eggs. Just keep stirring until it comes together before adding the next addition of eggs! Repeat until all the eggs are incorporated and you're left with a silky, pipe able dough. *(see notes)
Working with a piping bag fitted with a large star tip, fill your choux dough into the bag. Pipe 4 inch logs onto your prepared baking sheets, leaving about 1 inch of space in between each one. If you have any sharp edges peaking out, wet your fingers with water and press down any rough edges (they tend to burn).
Bake your éclair shells in the center of your preheated 375°F for 25 minutes. After 25 minutes, go in and carefully poke holes on the tips of your éclair shells with a skewer to allow steam to escape.
Continue baking for another 10 minutes, or until the shells turn a deep golden brown. The shells should also sound hollow when tapped. Take the shells out of the oven and cool completely to room temperature before filling.