Step 1: Preheat your oven to 375°F (190°C). Line two baking sheets with parchment paper or silicone baking mats.
Step 2: In a medium bowl, whisk together the fine cornmeal, all-purpose flour, baking powder, and salt. Set aside.
Step 3: In a large bowl, using an electric mixer, cream together the softened unsalted butter, granulated sugar, and light brown sugar on medium speed until light and fluffy, about 2-3 minutes. Scrape down the sides of the bowl as needed.
Step 4: Beat in the large egg and vanilla extract until well combined and smooth.
Step 5: Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined. Do not overmix.
Step 6: Drop rounded tablespoons of dough onto the prepared baking sheets, leaving about 2 inches between each cookie.
Step 7: Bake for 10-12 minutes, or until the edges are golden brown and the centers are just set. The cookies may still look slightly soft in the middle.
Step 8: Remove the baking sheets from the oven and let the cookies cool on the sheets for 5 minutes before transferring them to a wire rack to cool completely. Store in an airtight container.