Preheat the oven to 400 degrees F. Whisk the cornmeal, flour, sugar, baking powder, baking soda and salt in a medium bowl.
Cook 6 tablespoons butter in an 8-inch cast-iron skillet over medium heat until browned, about 5 minutes; remove from the heat. Whisk the eggs and honey in a bowl, then whisk in the milk, sour cream and browned butter. Add to the flour mixture and stir with a wooden spoon until just combined.
Heat the remaining 2 tablespoons butter in the skillet over medium heat until it foams. Remove from the heat and add the batter. Transfer to the oven; bake until the cornbread springs back when pressed, 20 to 30 minutes. Let cool 15 minutes in the skillet before slicing.