Preheat the oven to 400°F (200°C). Prepare an 8×8-inch square baking dish by greasing it thoroughly or lining it with parchment paper for easy removal after baking.
In a large mixing bowl, blend together the all-purpose flour, cornmeal, granulated sugar, baking soda, and salt until the mixture is uniform and dry ingredients are well distributed.
In a separate bowl, combine the sour cream, beaten eggs, melted butter, milk, and vanilla extract (if using). Whisk until the mixture is smooth and fully incorporated.
Gradually add the wet ingredients to the bowl of dry ingredients. Use a rubber spatula or wooden spoon to stir just until the batter comes together; small lumps may remain — avoid overmixing.
Transfer the batter into the prepared baking pan, smoothing the top with a spatula to ensure even baking. Place in the preheated oven and bake for 23 to 27 minutes, or until the surface is golden brown and a toothpick inserted into the center emerges clean.
Allow the cornbread to cool in the pan for about 10 minutes. Slice into squares and serve warm, optionally accompanied by butter, honey, or a drizzle of maple syrup.