1. Beat the softened butter and powdered sugar together until smooth, pale, and creamy.

2. Mix in the lemon zest and vanilla extract until fragrant.

3. In a separate bowl, whisk together the flour, cornstarch, and salt.

4. Add the dry ingredients to the butter mixture and mix on low speed just until a soft dough forms.

5. Cover and chill the dough for 30 minutes, or until firm enough to scoop.

6. Preheat the oven to 350°F and line baking sheets with parchment paper.

7. Scoop the dough into small balls and place them on the prepared baking sheets.

8. Gently flatten the tops slightly with your fingers or the bottom of a glass.

9. Bake for 10 to 12 minutes, until the cookies are set and the bottoms are lightly golden.

10. Let the cookies cool on the baking sheet for 5 minutes, then transfer them to a wire rack.

11. Whisk powdered sugar, lemon juice, and heavy cream or milk until smooth.

12. Drizzle the glaze over completely cooled cookies and sprinkle with fresh lemon zest.

13. Let the glaze set before serving or storing.