Gather the ingredients.

Preheat the oven to 350°F and position racks in the upper and lower thirds. In a large bowl, using a handheld electric mixer, beat the butter with the powdered sugar until very smooth, about 2 minutes.

Beat in the lemon zest and juice, then beat in the flour and salt until just incorporated; scrape down the side of the bowl as necessary.

Roll half of the dough into 1-inch balls. Arrange the balls 1 inch apart on two baking sheets and, using your fingers, gently flatten each cookie.

Bake for 12 to 14 minutes, until the cookies are lightly browned on the bottom and just firm; shift the baking sheets from top to bottom and front to back halfway through baking. Let the cookies cool on the baking sheets for 2 minutes, then transfer them to a rack to cool completely. Let the baking sheets cool slightly, then repeat with the remaining dough.

Meanwhile, make the glaze. In a bowl, whisk the powdered sugar with the lemon juice and butter until smooth.

Spread the lemon glaze on the cooled cookies and garnish with finely grated lemon zest. Let stand until the glaze is set, about 15 minutes.