Position an oven rack in the upper third and preheat to 325°F (163°C). Line two baking sheets with parchment paper.

In a mixing bowl, beat softened butter until light and fluffy, about 2-3 minutes. Gradually add powdered sugar, then incorporate cornstarch, vanilla extract, and kosher salt. Stir in all-purpose flour until a soft dough forms.

Form small balls of dough (about the size of a tablespoon) and roll in granulated sugar. Arrange on the baking sheets with at least 2 inches between each cookie and lightly flatten.

Bake for 18-22 minutes until lightly golden around the edges but still soft in the center. Cool cookies on a wire rack.

In a microwave-safe bowl, combine diced strawberries and granulated sugar. Heat for about 1 minute and strain to separate syrup from solids.

Mix fresh lemon juice with the strawberry syrup and gradually add powdered sugar until desired icing thickness is reached.

Spread icing over cooled cookies and allow to set for about 30 minutes at room temperature.