First, pre-heat oven to 435 degrees F. Then line 2 baking sheets with parchment paper.
In a medium pot, melt the butter, water and salt together over medium-low heat. Add the flour and stir with a spoon until everything is mixed together and forms a dough. Continue to cook dough for 2 minutes, making sure there is no raw flour left.
Next, add the eggs 1 at a time and continue mixing with a spoon until everything is well incorporated. It may look a but wet, but the dough will come does come together.
Next, secure a piping bag with a large round tip (or use a Ziploc and cut a small whole in 1 of the corners) and fill bag 3/4 full with the dough. (You may have re-fill bag several times). And pipe pate choux into 6 inch long. You can fit 11-12 on each baking sheet.
When all the pastry is piped out, brush the tops of each pate choux with water and bake at 425 degrees F for 10minutes then reduce the heat to 250 degrees F and continue baking for another 20 minutes or until all the pate choux is golden brown. When done, remove from oven and allow to cool completely.
Pastry Cream (Make ahead!)
Add all of the pastry cream ingredients to a medium saucepan and cook on medium heat, stirring everything together. Continue to cook, while stirring, until mixture thickens and is able to coat the back of a spoon.
When done, strain cream mixture through a fine mesh sieve and into another bowl. This will help remove any lumps or eggs that may have scrambled. Place plastic wrap directly over the cream, making sure it touches so no "skin" forms and chill in refrigerator until completely cool. (Note* The longer it sits, the thicker cream will get and easier it is to pipe into pastry).
In a small pot, add the sugar and cook on low heat until sugar gets clumpy. Use a wooden spoon to help break up the sugar to cook evenly. Continue to cook until sugar is completely smooth and turns a light brown color.
Then, add 1/4 cup butter, vanilla and heavy cream and continue to stir together. Add flaky sea salt and taste for seasoning. Turn off heat and continue to mix together until sauce thickens. Set aside.
Use a chopstick or skewer and poke holes on each side of the pate choux so there is a whole going through.
Fill a piping bag with pastry cream and pipe cream into pastry, trying not to overfull.
Then dip one side of the eclair into the caramel sauce. Or you can use a spoon to spoon over the top.
Garnish with extra sea salt or edible sprinkles.
A Few Notes:1) Make pastry cream the night before or day in advance so it has time to cool completely and thicken. 2) The longer the caramel sits, the thicker it will become.