How to Make It
Preheat the oven to 350°. Spread the chickpea flour on a rimmed baking sheet and toast for about 15 minutes, stirring occasionally, until lightly browned. Reduce the oven temperature to 325°.
Meanwhile, sift the sugar and all- purpose flour into the bowl of a stand mixer. Carefully sift in the hot chickpea flour.
In a saucepan, bring the butter just to a boil with the salt. Turn the mixer to its next-to-lowest speed and slowly drizzle the hot butter into the flour mixture. Continue beating the dough at this speed until it forms a solid ball, about 20 minutes.
Scrape the dough out onto a sheet of parchment paper and cover with another sheet of parchment paper. Roll out the dough into a 3/4-inch-thick rectangle. Peel off the top layer of parchment paper, transfer the dough to a baking sheet and refrigerate until firm, about 20 minutes.
Line another baking sheet with parchment paper. Cut the dough into 1-inch squares and arrange at least 1 inch apart on the lined baking sheets. Bake for about 10 minutes, until the squares are lightly browned at the edges; rotate the baking sheets from front to back and top to bottom halfway through baking. Transfer the shortbreads to a rack and let cool to room temperature before serving.