In a stand mixer, combine the softened cream cheese, granulated sugar, and softened butter. Beat on medium speed until the mixture is smooth and creamy, about 2-3 minutes.

Incorporate the egg, lemon juice, and lemon zest into the cream mixture. Continue mixing until everything is fully integrated.

Gradually add the all-purpose flour, baking soda, salt, and cornstarch to the wet mixture. Stir slowly until just combined.

Cover the mixing bowl with plastic wrap and refrigerate the dough for 45 minutes to 1 hour.

Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.

Using about 1.5 tablespoons of chilled dough for each cookie, roll them into balls and place them on the prepared baking sheet.

Bake in the preheated oven for 11-13 minutes until lightly golden around the edges.

Allow the cookies to cool on the baking sheet for about 5 minutes before transferring them to a wire rack.

Whisk together powdered sugar, additional lemon juice, and milk for the glaze until smooth yet pourable.

Once the cookies are completely cooled, drizzle the glaze over each cookie and allow it to set for about 10-15 minutes.