Place the butter into a saucepan over medium heat.

Allow the butter to melt completely, stirring occasionally.

The butter will begin to foam and crackle. Continue stirring frequently as the milk solids sink to the bottom.

After several minutes, the butter will turn golden brown and smell warm and nutty.

Once brown flecks appear on the bottom of the pan, immediately remove from the heat.

Pour the browned butter into a heat-safe bowl and allow it to cool before using in the cookie dough.

In a medium bowl, whisk together the flour, cornmeal, baking soda, baking powder, cornstarch, and salt. Set aside.

In a large mixing bowl, whisk together the cooled browned butter, brown sugar, and granulated sugar until smooth and glossy.

Add the eggs and egg yolk, mixing until fully combined.

Whisk in the vanilla extract and active sourdough starter until smooth and there are no lumps.

Gradually fold the dry ingredients into the wet ingredients until a thick cookie dough forms. Do not overmix.

Cover the bowl tightly with plastic wrap or a lid and refrigerate overnight for the natural fermentation process. If you are using sourdough discard, you'll still want to chill the cookie dough for 1-2 hours. This helps prevent the cookies from spreading too much while baking.

Preheat the oven to 350°F (177°C).

Line a baking sheet with parchment paper.

Scoop the cookie dough into large cookie dough balls 9about 3 tablespoons each) and place them onto the prepared baking sheet, leaving space between each cookie.

Bake for 11–13 minutes, or until the edges are lightly golden and the centers look just set.

Immediately after baking, use a large biscuit cutter, mug, or drinking glass to gently swirl around each cookie to shape them back into perfect circles.

Allow the cookies to cool completely before frosting.

In a large bowl, beat the softened butter until smooth and creamy.

Add the honey and vanilla extract and mix until combined.

Gradually add the powdered sugar, beating until light and fluffy.

Frost the cooled cookies using an offset spatula.

Finish with a drizzle of extra honey over the frosting.