Remove the butter from the fridge 45 minutes to an hour before starting. It should be soft enough to leave an indent from your finger but not greasy. Wash and dry the lemons. Then, use a microplane to zest them. Zest the lemons before you juice them; it's easier that way. Set the zest and juice aside.

In a large mixing bowl, beat the softened butter and powdered sugar until smooth. Use a hand mixer on medium speed for 2 to 3 minutes until the mixture is pale, light, and fluffy. This creates a soft base for the cookies, so take your time.

Add the lemon zest, lemon juice, vanilla extract, and lemon extract (if using) to the bowl. Mix on low speed until everything combines. Use a spatula to scrape the sides of the bowl to ensure nothing is missed.

In another bowl, whisk together the all-purpose flour, cornstarch, and salt. Add this dry mixture to the butter mixture all at once. Mix on the lowest speed until a soft dough forms. Stop mixing as soon as the flour disappears. The dough should be soft and slightly sticky.

Scoop the dough onto plastic wrap. Shape it into a log or press it into a flat disk. Wrap it tightly and refrigerate for at least 30 minutes. Chilling firms the dough, helping the cookies keep their shape while baking. You can also chill it overnight for easier handling.

Preheat your oven to 350°F. Line baking sheets with parchment paper. Use a small cookie scoop or a teaspoon to scoop the chilled dough into balls about 1 inch wide. Roll each ball between your palms to smooth it. Place them about 1.5 inches apart on the baking sheet and slightly flatten the tops with a spoon or your palm.

Bake at 350°F for 11 to 13 minutes. The cookies are done when the edges look set, and the tops appear dry, but they should stay very pale with no golden color. Overbaking will make them dry and crumbly instead of tender.

Let the cookies cool on the baking sheet for 5 minutes, then transfer them to a wire rack. They are fragile when hot, so handle them gently. Once completely cool, dust them generously with powdered sugar using a sifter, or drizzle with optional lemon glaze. Either option adds sweetness and looks nice.