Preheat your oven to 350°F. Line a baking sheet with parchment paper. This ensures that your cookies won't stick and will bake evenly.
In a medium bowl, whisk together the all-purpose flour, cornmeal, poppy seeds, baking soda, and sea salt. This mixture will add structure to your cookies.
In a stand mixer fitted with the paddle attachment, cream together the unsalted butter, granulated sugar, lemon zest, and orange zest on medium speed until the mixture is light and fluffy. This step is crucial as it incorporates air for a lighter cookie.
Add the olive oil, egg, and fresh lemon juice to the butter mixture. Continue mixing until fully combined and pale in color, scraping down the sides as needed. You want everything to blend nicely.
Gradually add the dry ingredients to the creamed mixture, mixing on low speed until just combined. Be careful not to overmix; the dough will be dense.
Using a ¼-cup sized cookie scoop, scoop the dough onto the prepared baking sheet. Remember, these cookies will spread, so leave some space between each scoop.
Sprinkle the tops of the cookies with a little extra granulated sugar for a sweet crust.
Bake in the preheated oven for 12 minutes. The cookies should be lightly golden. They might look like they need another minute, but trust the process and take them out.
Let the cookies cool on the baking sheet for about 1 minute before transferring them to a cooling rack to cool completely. This step helps them set properly.