1. Combine Dry Ingredients (Shortbread):

In a medium bowl, whisk together the all-purpose flour and cornstarch until well combined.

2. Cream Butter and Sugar:

In a stand mixer fitted with the paddle attachment (or using a hand mixer and a large bowl), beat together the softened butter, granulated sugar, and lemon zest over medium speed until creamy, 3 to 4 minutes.

Scrape the bottoms and sides of the bowl with a rubber spatula.

Beat in the fresh lemon juice and vanilla extract until well combined.

3. Gradually Add Dry Ingredients:

With the mixer on low speed, gradually add the flour mixture to the butter mixture.

Beating until just combined after each addition. Be careful not to overmix the dough.

4. Chill the Dough:

On a lightly floured work surface, place the dough.

Divide the dough in half. Form each half into a disk.

Wrap each disk in plastic wrap. Refrigerate until firm, 30 minutes to 1 hour. This chilling step is important for preventing the cookies from spreading too much during baking.

5. Preheat Oven and Prepare Baking Sheets:

Place one oven rack in the upper third of the oven and a second oven rack in the lower third of the oven.

Preheat the oven to 375°F (190°C).

Line 2 baking sheets with parchment paper.

6. Roll Out and Cut the Dough:

Working with 1 disk of dough at a time (keeping the second disk refrigerated), lightly flour a work surface.

Roll the dough out to ¼-inch thickness.

If using, press a floured cookie stamp into the dough to make an impression.

Use a 2- to 3-inch cookie cutter to cut the dough into circles (or your desired shape).

7. Transfer and Bake:

Using a thin spatula, transfer the cookies to the prepared baking sheets. Spacing them about 2 inches apart.

Refrigerate the scraps while you work with the second disk of dough.

Bake the cookies until the tops are dry and the bottoms begin to turn golden, 9 to 10 minutes.

8. Cool the Cookies:

Let the cookies cool for about 5 minutes on the baking sheets.

Then transfer them to a wire rack to cool completely.

Repeat with the remaining dough and scraps, rerolling only once for smooth cookies.

9. Make the Glaze:

While the cookies are cooling, make the glaze.

In a medium bowl, combine the powdered sugar, melted butter, and 1 tablespoon of the fresh lemon juice.

Whisk until smooth.

Add the remaining lemon juice, 1 teaspoon at a time, until the icing falls off the whisk in a fluid stream and the fallen ribbon of icing holds its shape for only a few seconds before sinking back into the bowl of icing. If the glaze is still not thin enough, add water, 1 teaspoon at a time.

10. Glaze the Cookies:

Working with one completely cooled cookie at a time, use a pastry brush to brush a thin layer of glaze onto each cookie.

If the pastry brush is leaving behind too many streaks or the glaze feels too thick, whisk in another teaspoon of water.

11. Set and Store:

Allow the glazed cookies to set for 15 minutes.

Store the cookies at room temperature in an airtight container for up to 1 week. Enjoy!