Heat the oven to 150 C / 300 F. Line a 33 x 46 cm / 13 x 18-inch sheet pan with parchment paper.
Toast the hazelnuts in a dry skillet over medium heat for 4 to 5 minutes, until fragrant and the skins blister. Wrap in a kitchen towel and rub to remove most of the skins, then chop roughly.
Whisk the egg whites and salt in a mixing bowl until foamy and loose, not stiff peaks.
Add the sugar and vanilla extract and whisk to combine. Fold in the chopped hazelnuts until evenly coated.
Transfer the mixture to a 26 cm / 10-inch heavy-bottomed saucepan set over low heat. Cook, stirring constantly with a wooden spoon, for 10 to 15 minutes, until it turns pale gold, pulls away from the sides of the pan, and smells toasted rather than raw. This step goes wrong fast if the heat's too high, the egg white scrambles into dry curds instead of turning glossy and thick, so keep the burner low and don't stop stirring.
Remove the pan from the heat. Drop heaping tablespoons of the warm mixture, about 25 g each, onto the prepared sheet pan, spacing them 4 cm / 1.5 inch apart.
Bake for 20 to 25 minutes, rotating the pan once, until deeply golden brown and cracked on top.
Cool the cookies on the pan for 10 minutes, then move them to a wire rack to cool completely. They firm up as they cool, crisp outside, chewy inside.