Spread the hazelnuts on a baking sheet and bake until golden brown, about 10 minutes; let cool, then finely chop.
Whisk the flour, allspice, salt and hazelnuts in a medium bowl. Beat the butter and 1/4 cup confectioners' sugar in a large bowl with a mixer on medium speed until light and creamy, about 3 minutes. Beat in the vanilla. Reduce the mixer speed to low and gradually beat in the flour mixture until the dough comes together. Cover with plastic wrap and refrigerate until firm, at least 1 hour or overnight.
Preheat the oven to 350 degrees F. Coat a baking sheet with cooking spray. Roll tablespoonfuls of the dough into balls and arrange 1 inch apart on the prepared baking sheet. Bake until light golden on the bottom, about 12 minutes. Meanwhile, sift the remaining 3/4 cup confectioners' sugar into a medium bowl.
Immediately transfer the warm cookies to the bowl of confectioners' sugar and gently toss to coat; transfer to a rack to cool completely. Roll the cookies in confectioners' sugar again when completely cool.