With the rack in the middle position, preheat the oven to 170°C (325°F). Line the bottom of a 20-cm (8-inch) square cake pan with parchment paper, letting paper extend over two opposite sides. Butter the two other sides.
In a bowl, combine flour and salt. Set aside.
In another bowl, beat eggs, hazelnut spread, brown sugar and vanilla extract with an electric mixer until smooth, about 2 minutes. With the mixer on low speed, add flour mixture, alternating with melted butter.
Scrape batter into the cake pan. Bake until a toothpick inserted in the centre comes out with a few crumbs attached (not completely clean), 35 to 40 minutes.
Cool in the pan for about 2 hours. Unmould and cut into squares.