Whisk together the flour, cornstarch, and salt in a medium bowl; set aside.
In a stand mixer fitted with the paddle (or with a hand mixer), beat the butter and granulated sugar on medium speed until smooth and creamy, about 2 minutes. Mix in the lemon extract and vanilla until combined.
Add the lemon zest and mix just 10–15 seconds to distribute the oils without overworking the butter.
Add the dry ingredients all at once. Mix on low, pulsing if needed to avoid a flour cloud, until the dough looks sandy and starts to clump. Stop as soon as it holds together when pinched—do not overmix.
Divide dough in half. Press each portion into a 1-inch-thick disk, wrap tightly, and chill until firm enough to roll, 45–60 minutes.
Preheat the oven to 350°F (177°C). Line 2 baking sheets with parchment paper.
Working with one disk at a time, roll the dough between two sheets of parchment to 3/8-inch thickness. Cut 2-inch rounds, gathering and rerolling scraps once if needed. Arrange on prepared sheets about 1 inch apart, then chill the cutouts for 10 minutes for the cleanest edges.
Lightly brush the tops with water and sprinkle generously with turbinado sugar.
Bake 12–15 minutes, rotating pans halfway, until the rims are just turning pale golden and centers look set. Cool on the sheet for 5 minutes, then transfer to a rack to cool completely.