Make the brown butter: Melt butter in a small stainless steel skillet, whisking constantly. As it simmers, it will start to form bubbles and pop, and golden brown specks will form. It should smell like toffee and a little nutty. This means it’s ready - be careful not to let it burn. Transfer to a bowl and let cool for 20 minutes. Note 1: A stainless steel or white ceramic skillet will help you see the golden specks better. Note 2: If you prefer not to use brown butter, you can simply use melted butter.
Preheat oven to 400 degrees F. Place a 9-inch cast iron skillet in the oven to get it really hot.
Mix dry ingredients: In a large bowl, whisk flour, cornmeal, sugar, baking powder, baking soda, and Kosher salt. Set aside.
Mix wet ingredients: In a separate large bowl, whisk the buttermilk, whole milk, and eggs until combined. Then, drizzle in brown butter (or the simple melted butter) and whisk until evenly combined. The butter may solidify a bit, don’t worry, but try to break it up a little with the whisk.
Add the dry ingredients into the wet ingredients. Mix until evenly combined and no pockets of flour remain. Do not overmix.
Remove the hot skillet from oven. Grease with 1 tablespoon of butter and wipe off any excess with paper towel so it doesn't pool over the batter. Immediately, pour the batter into the hot greased skillet.
Bake for about 20-23 minutes, or until a toothpick or cake tester inserted in the middle comes out clean and the top is golden brown.
Let rest for 15 minutes before serving. If desired, serve with butter and a drizzle of honey. Enjoy!