Sift the flour into a large mixing bowl. Add the salt and stir to combine.
Gradually pour in the water, whisking continuously until the batter is smooth and lump-free. It should be fluid but not too runny. Cover and let it rest for 1 hour.
Heat a skillet well and lightly grease the bottom with olive oil.
Pour in enough batter to form a layer about 5 mm (1/4 inch) thick. Cook over low heat, covered, for about 5 minutes, or until the surface is set. Flip the testarolo and cook for 1 more minute. Remove from the pan and let cool.
Just before cooking, cut the testaroli into pieces (traditionally into diamond shapes about 4-5 cm/1.5-2 inches per side).
To cook the testaroli, bring a pot of water to a boil, add salt, then turn off the heat. Add the testaroli and let them sit in the hot water for 1–2 minutes. Then drain gently. Be careful not to overcook them — they may fall apart and turn into a floury soup!