Position a rack in the center of the oven and preheat to 325°F (165°C). Line two baking sheets with parchment paper.
In a large bowl, combine the granulated sugar for the dough with the zest of 2 lemons. Use your fingertips to rub the zest into the sugar until it’s fragrant and slightly damp—this blooms the citrus oils.
In a separate bowl, whisk together the flour, cornstarch, baking powder, and salt; set aside.
Beat the butter with the lemon sugar on medium speed until very light and fluffy, 2 to 3 minutes. Scrape down the bowl. Add the egg, egg yolk, vanilla, and lemon extract; beat until smooth and creamy, about 45 seconds.
Add the dry ingredients in two additions on low speed, mixing just until no streaks of flour remain. If the dough feels soft or sticky, refrigerate for 10 to 15 minutes while you prepare the coating (chilled dough bakes thicker and more evenly).
Stir together the coating sugar and 1 teaspoon lemon zest in a shallow bowl. Scoop the dough into 1 1/2-tablespoon portions (about 30 g), roll into balls, and coat generously in the lemon-sugar. Arrange 2 inches apart on the prepared sheets, then gently press each ball to about 1/2-inch thickness with the bottom of a glass for an even crinkle.
Bake one sheet at a time until the edges are set and just barely turning golden and the centers look puffy but soft, 12 to 14 minutes at 325°F. Do not overbake.
Cool on the baking sheet for 5 minutes, then transfer cookies to a wire rack to finish cooling. Repeat with remaining dough.