Beat the softened butter and powdered sugar until smooth and creamy, about 2 minutes. Mix in the lemon zest and fresh lemon juice until evenly distributed.

Whisk together the flour, cornstarch, and salt in a separate bowl. Add the dry mixture to the butter mixture and mix just until a soft dough forms.

Divide the dough in half and shape each portion into a log approximately 1 1/2 inches in diameter. Wrap the logs and refrigerate for at least 30 minutes, or until firm.

Heat the oven to 350°F (175°C) and line baking sheets with parchment paper. Slice the chilled logs into rounds about 1/4 inch thick and arrange them on the prepared sheets.

Bake for 10–12 minutes per tray, watching closely so the cookies remain pale with edges that are just set and very lightly colored. Cool them on the baking sheet for several minutes, then transfer them to a rack to cool completely.

Whisk the glaze ingredients until smooth, then drizzle or spread the glaze over the completely cooled cookies. Let the glaze set before serving or stacking.