Whisk together flour, cornstarch, and salt; set aside.

In mixer, beat butter until smooth. Add powdered sugar and beat until light and fluffy.

Mix in lemon zest, then slowly add lemon juice while mixing.

Gradually add flour mixture on low speed until fully incorporated. Scrape bowl; cover and refrigerate dough for 30–60 minutes.

Scoop tablespoon-sized balls, roll and place on parchment‑lined baking sheet. Press gently to flatten tops. Chill entire sheet in fridge or freezer while oven heats.

Preheat oven to 350 °F (175 °C). Bake cookies for 11–13 minutes, until edges turn golden. Let cool briefly on sheet, then transfer to wire rack.

Meanwhile, whisk glaze ingredients; add more lemon juice if needed to reach drizzling consistency.

Dip cooled cookies into glaze, then return to rack to allow glaze to set before storing.