Make the dough: Spray two (18 x 13-inch) half-sheet pans (or other large baking pans with sides) with nonstick coating or line with silicone mats or parchment paper. Note: DO NOT PREHEAT THE OVEN. If possible, set each baking pan inside a second pan so the cookie bottoms bake evenly without burning on the bottom.

Whisk together the dry ingredients: flour, semolina, baking powder, and salt.

In the bowl of a standing mixer fitted with the paddle attachment, combine the butter, confectioners’ sugar, vanilla, eggs, egg white, and lemon zest, and beat until well combined, 5 to 6 minutes, scraping down the sides once or twice. Add the flour mixture and beat again, just long enough for the dough to come together and form a ball.

Dust your hands and a work surface with flour and form the dough into two long, thin logs, about 1 inch in diameter. Cut the logs into 1-inch sections and shape each section into walnut-sized balls. Toss the balls lightly but vigorously onto the baking pans so they stick to the pan and flatten slightly in alternating odd and even rows. Rearrange if necessary so the balls are evenly spaced.

Press one hazelnut, with the pointy side facing up, into the center of each dough ball, so the tip of the hazelnut is at the same level as the cookie. Mix the egg yolk with 1 teaspoon water and brush the cookies lightly but evenly with the mixture, making sure that excess egg yolk doesn’t pool into the center.

Place the trays in the oven and set the oven temperature to 400°F. Bake the cookies for 30 to 35 minutes or until the tops of the cookies are light golden and crackled, rotating the trays from front to back and from the top to bottom shelves after 15 minutes.

Make the syrup: NOTE: The syrup must be ready and hot when the cookies come out of the oven. Combine 3 cups water and the sugar in a medium heavy-bottomed pot. Bring to a boil over medium heat then simmer for 2 minutes or until the syrup is completely clear. Remove from the heat and combine with the lemon juice.

As soon as the cookies come out of the oven, pour all the hot syrup over them, making sure that all the cookies are evenly drenched in the syrup. There should be about 1/2 inch of syrup in the pans, which will be absorbed by the cookies as they cool.

Make the garnish: Cool the cookies to room temperature, then sprinkle with the pistachios before serving. Store covered and at room temperature for up to three days.