In a medium bowl, whisk the flour, cornstarch, baking soda, and salt together. Set aside.
In a large bowl using a handheld or stand mixer fitted with a paddle attachment, beat the butter, sugar, and lemon zest together on medium-high speed until creamed, about 3 minutes. Add the egg, lemon juice, and vanilla extract and beat on medium-high speed until combined, about 1 minute. Scrape down the sides and bottom of the bowl and beat again as needed to combine. The mixture will look curdled; that’s ok.
Add the dry ingredients to the wet ingredients and mix on low speed until combined. Dough will be thick and sticky. Cover and chill cookie dough in the refrigerator for at least 2 hours (and up to 3 days).
Preheat the oven to 350°F (177°C). Line baking sheets with parchment paper or silicone baking mats. If the dough has chilled for longer than 2 hours, let it sit at room temperature for about 15 minutes.
Scoop dough, about 1.5 Tablespoons (30g) of dough each, and roll into balls. Arrange cookies 3 inches apart on the baking sheets.
Bake for 11–13 minutes or until lightly browned around the edges. The centers will look very soft and slightly underbaked. That’s key for a soft texture. Do not over-bake.
Remove from the oven and allow cookies to cool on the baking sheet for 5 minutes before transferring to a cooling rack to cool completely.