Put the milk, water, salt, sugar and butter in a pot and heat them on medium heat until the butter melts and mixture starts to boil. Once boiling, add in all the flour at once and stir energetically to get a ball of choux pastry.
Stir another 3-4 min. on the stove and remove the pot. Leave the choux pastry to cool. Once it has, add the eggs 1 by 1, stirring well after each until it absorbs each egg entirely.
Pour the mixture into a pastry bag and pipe out small balls or elongated eclairs onto a sheet of baking paper in a tray (with spaces in between them). Bake in a preheated 356°F (180 °C) oven about 25-30 min. Do not open the oven while the eclairs are baking.
For the cream, pour the milk in a pot and heat it up. In the meantime, mix the eggs and sugar. Beat with a mixer until the mixture turns a light color. Add the flour and corn starch. Beat with a mixer on a lower speed or by hand.
To make the temperatures uniform, add 1 ladle of warm milk to the egg/flour mixture. Stir well. Repeat. Pour the diluted mixture in a thin trickle to the boiling milk, while stirring nonstop. Finally, add the 2 vanillas and butter and stir until the butter is melted and absorbed by the cream.