Whisk flour and salt in a large bowl, then gradually whisk in water until the batter is smooth and thin, like heavy cream.

Cover the bowl and let the batter rest at room temperature for 30 minutes so the flour hydrates fully.

Heat a 10-inch nonstick or cast-iron crepe pan over medium heat and brush lightly with olive oil.

Ladle in about 120 ml of batter, tilt the pan to spread it thin, cover, and cook for 3 to 4 minutes until the top looks dry and set.

Flip carefully and cook uncovered for 1 to 2 minutes until both sides have light brown spots. Repeat with the remaining batter, stacking cooked sheets on a rack to cool completely, about 5 to 6 sheets total.

Pulse basil, garlic, and pine nuts in a food processor until coarsely chopped.

Add parmesan and pecorino, pulse again, then drizzle in olive oil while pulsing until the pesto is thick but pourable. Season with salt.

Cut the cooled testaroli sheets into rough 2-inch diamonds or squares.

Bring a large pot of water to a boil and salt it generously, then drop in the testaroli pieces.

Cook for 60 to 90 seconds, just until the pieces float and turn slightly translucent at the edges, then scoop out with a slotted spoon, reserving 1/2 cup of the poaching water.

Toss the warm testaroli with pesto in a large bowl, adding a splash of reserved water to loosen the sauce. Serve right away with extra parmesan.