Sift the powdered sugar for the glaze into a small bowl to remove lumps, then set aside. Finely grate the lemon zest directly onto the granulated sugar in a medium bowl. Using your fingertips, gently rub the zest into the sugar for about 30 seconds until the mixture becomes fragrant and the sugar takes on a pale yellow color—this releases the lemon oils and distributes flavor evenly throughout your cookies. I like to use a microplane grater because it captures the brightest, most aromatic zest without the bitter white pith.
Add the softened butter and kosher salt to the lemon-sugar mixture. Using an electric mixer on medium speed, beat for about 2 minutes until the mixture is pale, fluffy, and completely smooth. Scrape down the bowl with a spatula to ensure even mixing. Add the egg yolk and 2 teaspoons of fresh lemon juice, mixing on medium speed until fully combined. Switch to low speed, add the flour gradually, then increase to medium speed and mix until the dough just begins to form clumps and comes together—be careful not to overmix, as this keeps the shortbread tender and crumbly.
Turn the dough out onto a lightly floured surface and gently gather it together. Shape it into a rectangle about 1/2 inch thick, then lightly flour the top. Using a rolling pin, roll the dough to an even 1/4-inch thickness, working from the center outward. Cut out cookies using a 2-inch cutter, placing each one on a parchment-lined baking sheet spaced about 1.5 inches apart. Using a fork, prick each cookie 2-3 times to create a decorative pattern and ensure even baking. Transfer the sheet to the refrigerator and chill for at least 20 minutes—this prevents the cookies from spreading too much in the oven and helps them maintain their tender texture.
Preheat your oven to 300°F and line a fresh baking sheet with parchment paper. Remove the chilled cookies from the refrigerator and transfer them to the prepared baking sheet. Bake for 20-22 minutes until the edges are just barely golden but the centers remain pale and tender—the low temperature ensures these cookies stay delicate and buttery rather than crispy. The shortbread should look almost underbaked when you remove it from the oven.
While the cookies cool on the baking sheet for 5 minutes, prepare the glaze. Sift the powdered sugar from Step 1 into a bowl and add 4 teaspoons of fresh lemon juice, stirring until combined. Add additional lemon juice 1/2 teaspoon at a time, stirring well, until you reach a pourable but not too thin consistency—it should flow slowly off a spoon. I find that this amount of juice gives both great tang and a silky texture that sets nicely on the cookies. After 5 minutes on the sheet, transfer the still-warm cookies to a wire rack to cool completely.
Once the cookies are completely cooled, spread or drizzle the lemon glaze evenly over each cookie using a small spoon or pastry brush. Allow the glaze to dry completely at room temperature for about 30 minutes before serving or storing—this creates a beautiful, set finish that protects the delicate shortbread underneath.