Beat the butter, sugar, and lemon zest in a large bowl until pale and fluffy.

Mix in the flour and salt just until a dough forms.

Shape the dough into a 2-inch-wide log, wrap tightly, and chill at least 1 hour.

Preheat oven to 350°F (175°C). Slice the log into 1/4-inch-thick rounds and bake on lined sheets for 12 to 14 minutes until edges are golden. Cool completely.

Whisk powdered sugar with 2 tbsp lemon juice until smooth, adding more juice if needed. Drizzle over cooled cookies and let the glaze set.