Preheat the oven to 375°F.
Line an 8 x 8 or 9 x 9 baking pan with parchment paper or grease it to prevent sticking.
Begin by browning the butter. Heat the butter in a pan over medium heat for 5 to 6 minutes until it browns. Be careful not to burn it. Transfer to a bowl and let it cool.
In a large mixing bowl, whisk together the flour, cornmeal, salt, baking powder, baking soda, granulated sugar, and brown sugar.
Add the eggs, buttermilk, heavy cream, and browned butter to the bowl. Whisk until you have a very smooth batter consistency.
Transfer the batter to the prepared baking pan and bake for 25 to 28 minutes, or until a toothpick inserted into the center comes out clean.
While the cornbread bakes, make the honey butter by mixing melted butter and honey in a small bowl.
Once the cornbread is done, let it cool for 10 to 15 minutes, then slice and brush the top with honey butter. Optionally, sprinkle with flaky sea salt.
Enjoy warm!