1. Make the Cookie Dough:

1. In a large mixing bowl, cream the softened butter and powdered sugar together until light and fluffy.
2. Mix in the lemon zest, lemon juice, and vanilla extract until well combined.
3. In a separate bowl, whisk together the flour, cornstarch, and salt. Gradually add this dry mixture to the wet ingredients, mixing just until a soft dough forms.

2. Chill the Dough:

1. Divide the dough in half and shape each portion into a log about 1.5 inches in diameter.
2. Wrap the logs in plastic wrap and refrigerate for at least 1 hour, or until firm.

3. Slice and Bake:

1. Preheat your oven to 350°F (175°C) and line baking sheets with parchment paper.
2. Unwrap the chilled dough and slice into 1/4-inch thick rounds.
3. Place the cookies about 1 inch apart on the prepared baking sheets.
4. Bake for 10-12 minutes, or until the edges are just starting to turn golden. Let the cookies cool slightly on the baking sheets.

4. Coat the Cookies:

1. While the cookies are still warm, gently toss them in powdered sugar. For extra lemony flavor, mix the powdered sugar with additional lemon zest before coating.
2. Allow the cookies to cool completely on a wire rack. Toss them in powdered sugar again for a thicker coating, if desired.