Preheat oven to 325°F. Coat an 8 ½- x 4 ½-inch loaf pan with cooking spray. Whisk together flour, cornmeal, sugar, baking powder, baking soda, and salt in a large bowl. Whisk together eggs, buttermilk, and melted butter in a medium bowl. Stir egg mixture into flour mixture just until combined. Pour batter into prepared loaf pan; smooth top.
Bake in preheated oven until cornbread is light brown around edges and a wooden pick inserted in center of loaf comes out clean, about 35 minutes. Remove from oven; let cool in loaf pan 5 minutes. Invert cornbread onto a wire rack, and let cool completely, about 30 minutes. Cornbread may be stored in a ziplock plastic bag at room temperature up to 2 days.