Preheat oven to 350°F. Line two half sheet baking pans with a Silpat silicone mat or parchment paper.
In the bowl of a stand mixer with a paddle attachment (or in a large bowl using a hand mixer), cream the butter, sugar, and zest together until light and fluffy.
Beat in the lemon juice and salt. Add in the flour and mix until just combined.
Portion out cookies into two tablespoon balls using a medium cookie scoop. Flatten the cookies with a crosshatch pattern with a fork, then chill the cookies in the refrigerator for 20 minutes before baking.
Bake for 20 to 23 minutes or until the cookies' edges are lightly browned.
Allow the cookies to cool for 5 minutes on the baking pan, then move them to a cooling rack to cool completely.
Meanwhile, sift the powdered sugar into a small bowl. Mix two tablespoons of juice with the powdered sugar in a small bowl, adding more juice or powdered sugar as needed to achieve a drizzling consistency.
When the cookies are completely cooled, move them back to a cooled baking pan. Drizzle the cookies with the glaze and let set for 15 minutes. Serve and enjoy!
Chilling the cookies before baking firms up the butter and keeps the cookies from spreading too much.Meyer lemons have a softer, less acidic flavor than regular lemons, and using them will temper their influence, giving you balance between the lemon and butter. If you want that sharper tang, by all means use regular lemons!You can freeze the dough after portioning and flattening them. Lay them on a baking pan (I line the pan with waxed paper first) and place in the freezer until firm (about 45 minutes). Remove the now-frozen balls to a freezer-safe ziplock bag until ready to use. They'll keep 3 to 4 months, at least.To bake cookies from frozen, reduce the oven temperature to 325°F and bake about 5 minutes longer than normal. Follow the instructions for cooling and glazing.You can also freeze the baked cookies (glazed or unglazed). They should keep for at least 1 to 2 months.To make Lemon Shortbread bars, press the dough into an 8- x 8-inch baking pan (for thicker bars) or a 9- x 9-inch baking pan (for thinner bars) that's been lined with parchment paper, leaving an overhang. Pierce the dough with a fork, then chill for 20 to 30 minutes, or until the dough is firm. Bake at 350°F for 25 to 30 minutes, then cut into bars while they're still warm in the pan. Let the bars cool in the pan, then use the overhang to remove them from the pan.