Start with the pastry cream. Heat the milk in a saucepan until it begins to steam. Meanwhile, beat the yolks and the sugar until very thick and yellow. Add the flour, cornstarch and salt to the yolk mixture.
Very slowly, pour the steamed milk into the egg mixture, beating continuously. Rinse out the saucepan, pour the entire mixture back into it.
Heat over medium, stirring constantly, and bring mixture to a boil. Boil for 1 1/2 to 2 minutes to thicken. This will really get thick, so you may have to stop stirring for a few seconds to check and see if the cream is actually boiling.
Remove from heat, add vanilla extract. Store in a shallow bowl, covered with plastic wrap touching the surface of the cream. Refrigerate for at least 2 hours before using.
While the cream is chilling, begin preparing the pate a choux. Bring the water, butter, sugar and salt to a boil in a small saucepan. Add the flour to the boiling mixture all at once. Begin to stir over medium heat until mixture forms a ball and pulls away from the sides of the pot. After that happens, cook for another 2 minutes.
Transfer paste to a clean bowl, beat either by hand or with an electric mixture for 5-10 minutes to cool it off. Add eggs one at a time and beat until a shiny dough forms, about 5-10 minutes depending on whether or not you're using an electric mixer.
Spoon out 8 portions of the dough onto a prepared baking sheet. With damp fingers, shape the pieces into ovals, making sure to smooth out any cracks in the dough.
Bake for 10 minutes at 400 degrees, reduce heat to 350 and bake for 25 more minutes, turning halfway through so that they bake evenly. The eclairs should puff up a lot and be a nice golden color. With a toothpick, poke a hole in each eclair to help some of the steam escape, let cool completely.
While the eclairs are cooling, make the chocolate glaze. Microwave the chocolate and corn syrup together in 30 second intervals until the chocolate melts. Remove from microwave, add the butter and stir until everything is combined.
Once the pastries are cool, cut in half gently and spoon some of the pastry cream into them. Drizzle a little bit of glaze on each one. Let sit for about 20 minutes to allow glaze to set.
If you have any leftover eclairs, store in the fridge so that the cream doesn't separate! Enjoy!