Preheat oven to 350 degrees F.
Combine the cornmeal, flour, sugar, salt, baking powder, and baking soda in a large bowl.
In a small bowl, mix the eggs, buttermilk, and vanilla with a wooden spoon or dough whisk. Add to the dry ingredients and pour the melted butter over the top of the batter. Stir just until all ingredients are moistened yet thoroughly blended; take care not to overmix.
Pour the batter into a greased 8-inch round springform pan or square Pyrex pan.
Bake in the preheated oven about 40 to 45 minutes, until golden around the edges and a cake tester inserted into the center comes out clean. Let stand 15 minutes before cutting to serve.