Pour all the water into a large bowl.
Gradually, add all the flour. When adding the flour, keep whisking to avoid the formation of lumps.
Add the salt and give the final whisk to complete the batter. In the end you should have a batter more or less of the same consistency as batter you use to make pancakes.
Put a few drops of olive oil onto the pan surface (not too much).
Spread the oil around so that the surface is completely coated, then put the pan onto a medium/high heat.
When the pan is hot, pour enough batter onto its surface to make a testaroli disc of about 5 mm (3/16") thick.
Now, cook for about 2-3 minutes.
After few seconds, you will see the colour of the disc changing from white to yellowish.
Check (using a flat spatula) that the bottom surface of the disc has turned a kind of light brown colour (but not uniform) and then turn onto the other side.
We then cook the second side until it is a light brown colour.
When the testaroli disc is ready, put it onto a flat surface (I used a glass cutting board) and cut it into big rectangles, something like 7 x 4 cm (2 3/4" x 1 3/4") or diamonds.
Take a large pan and bring about 5 litres (5 quarts 3/4 cup) of water to the boil. Put some salt into the water, the same quantity you would use when boiling spaghetti.
Boiling the water...
When the water is boiling well, turn off the heat and quickly put your testaroli into the pan. The reason why we turn the heat off is because boiling would break the testaroli.
Leave the testaroli in the hot water for about 5-6 minutes. After this time you can see the testaroli starting to come to the surface, it is then time to take them out of the pan.
Meanwhile, you should have prepared your pesto sauce and diluted it with just a bit of the boiling water (something like 1 or 2 tablespoons) you used for boiling the testaroli. Put some pesto sauce in the bottom of a large deep dish.
Remove your testaroli from the pan using a slotted spoon.
Lay the testaroli down onto the bottom of the deep dish. Every layer should be covered with pesto sauce...
...and few drops of extra virgin olive oil. Keep layering in this way until all the testaroli are used.
Finally, sprinkle with Parmesan cheese and serve.