Preheat oven to 375 F° (175 C°). Grease an 8-inch square pan or cast-iron skillet.
Melt butter in a large skillet. Remove from heat and stir in sugar and honey. Quickly add eggs and beat until well blended. Combine buttermilk with baking soda and stir into mixture in pan. Stir in cornmeal, flour, and salt until well blended and little to no lumps remain. Pour batter into the prepared pan.
Bake in the preheated oven for 30 to 40 minutes, or until browned to your liking. With a toothpick, poke the center of the cornbread. If the toothpick comes out clean, the cornbread is ready.