Whisk together the flour, salt, baking powder and baking soda in a large bowl.
Beat together the brown sugar and butter in another large bowl with an electric mixer on medium-high speed until light and fluffy, about 4 minutes. Add the eggs 1 at time, beating after each addition to incorporate. Beat in the vanilla. Reduce the speed to medium, add the flour mixture and beat until just incorporated.
Divide the dough into 18 equal mounds, each about 2 tablespoons, and flatten slightly with wet hands. Put 2 teaspoons of the chilled chocolate-hazelnut spread in the center of each piece of dough, then press and pinch the cookie dough around the spread to form round and sealed balls. Chill for 30 minutes.
Meanwhile, position oven racks in the top and bottom thirds of the oven and preheat to 300 degrees F. Line 2 baking sheets with parchment.
Put 6 chilled dough balls onto each prepared baking sheet, spacing them about 2 inches apart. Bake, rotating the baking sheets halfway through, until the cookies are golden around the edges, about 20 minutes. Let the cookies cool for a few minutes on the baking sheets, then transfer to a rack or plate and serve warm if you'd like. When the baking sheets have cooled completely, bake the remaining 6 dough balls on one of the sheets, then let cool slightly.
Store the cookies in a tightly sealed container at room temperature for up to 5 days.
When measuring flour, we spoon it into a dry measuring cup and level off excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.)