In a large mixing bowl, beat the butter and confectioners sugar until light and fluffy. Mix in the lemon zest.

In a separate bowl, whisk to combine the flour, cornstarch, and salt.

With the mixer on low, gradually mix the dry ingredients into the wet ingredients, mixing until just combined.

Cover and refrigerate dough for 1 hour or until firm enough to handle.

Shape the dough into a roll approximately 1-3/4 inches in diameter.

Place the granulated sugar in a shallow pan. Roll the dough in the sugar until coated. Wrap the roll in plastic wrap and refrigerate for 2–3 hours until firm.

Preheat the oven to 375°F. Line baking sheets with parchment paper.

Unwrap the dough and slice into 1/4-inch thick slices. Place 1 inch apart on baking sheets.

Bake for 9–11 minutes, or until cookies are set. Note: They will not turn brown on the edges. They will only change color slightly.

Allow cookies to cool on baking sheets for 5 minutes before transferring to wire racks to cool completely.

In a small bowl, whisk to combine the confectioners' sugar, lemon juice, and grated lemon peel.

Spoon the glaze over the cooled cookies, using the back of the spoon to spread the icing out to the edges. Allow the icing to dry before serving or storing.