Baking these tender, slightly chewy treats twice, like biscotti, results in crisp, golden edges. We used Frangelico, a hazelnut liqueur, to flavor the cookies, but you could substitute other liqueurs, such as Nocello, Kahlua, or amaretto.
Preheat oven to 350 degrees. Butter an 8-inch square baking pan and dust with flour, tapping out excess. In a food processor, pulse almonds, hazelnuts, 1/3 cup sugar, and the salt until nuts are finely ground.
Beat butter and remaining 1/3 cup sugar with an electric mixer on medium-high speed until pale and fluffy, 3 to 4 minutes. Add eggs, 1 at a time, beating until thoroughly combined. Reduce speed to low; beat in nut mixture, then Frangelico. Transfer batter to prepared pan.
Bake, rotating pan halfway through, until top is golden and firm to the touch, and a wooden skewer inserted into center comes out clean, about 25 minutes. Let cool completely on a wire rack before removing cake from pan.
Cut cake into 1-inch-wide rows; cut rows on a diagonal at 1 1/2-inch intervals to create 1 1/2-by-1-inch diamonds. Press an almond sliver into top of each diamond. (At this point, cookies can be refrigerated in an airtight container up to 1 week.)
Remove diamonds from pan, and place on parchment-lined baking sheets, spacing 1 inch apart. Bake, rotating sheets halfway through, until edges are golden brown and crisp, about 20 minutes. Let cool completely on wire racks. Diamonds can be stored in an airtight container at room temperature up to 1 week.