Make the pate a choux: Preheat the oven to 350°F. Prepare a baking sheet with parchment paper or a silpat.
Sift the pastry flour and reserve in a bowl. Bring the milk, water, salt, sugar and butter to a boil in a small pot over medium heat. Remove from the heat, add the flour, and stir with a spatula or wooden spoon to combine. Return the mixture to the heat and cook the paste for 1 minute or until it clears the side of the pot, stirring occasionally.
Transfer the cooked dough to a stand mixer and with the paddle attachment, mix on low speed until the steam is gone (a few minutes). While the dough is mixing on low, temper the eggs by pouring 3/4 of the eggs into the dough and mix until combined. Add the remainder of the eggs and mix until just combined (dough will have a sheen to it).
Transfer the dough to a piping bag and pipe into the desired shape onto prepared pan and brush lightly with egg wash (optional). I piped mini eclairs about 2.5 inches long but they can be much larger.
Bake at 350°F in a convection oven for 10 minutes and then decrease the temperature to 325°F with the door slightly open for 15-20 minutes or until they are slightly brown on the exterior and "dry" in the center.
Make the pastry cream: Place the milk in a heavy bottomed saucepan and bring to a boil. Keeping an eye on the milk, whisk the cornstarch, sugar, and salt together in a bowl. Gradually add eggs to this mixture and mix until smooth.
Slowly add about one-third of the hot milk to the egg mixture while whisking rapidly (tempering the egg mixture so the eggs do not cook). Pour the tempered egg mixture back into the remaining milk. Place over medium heat and cook, stirring constantly, until the mixture comes to a boil and thickens. You know that it is ready when it is thick enough to stick to the back of a wooden spoon without sliding off quickly. Stir in the vanilla extract, then the butter until fully incorporated.
Pour the pastry cream into a bowl and cover with a piece of parchment paper until cool. When fully cooled, store in the refrigerator with plastic wrap. If stored properly, pastry cream will keep fresh for up to three days (but definitely best on day one).
To serve: To assemble the eclairs, fill a piping bag with a small tip and some pastry cream and lightly poke a hold in the end, or bottom of the cooked shells and gently add the cream until you feel it puff up. You can also slice the shells in half, lengthwise, and spoon the pastry cream onto the bottom layer and then sandwich the two layers back together.
If you so desire (and why wouldn't you?), you can add some melted chocolate to the top.
