Preheat the oven to 400°F (200°C) and grease a square or round cake pan and set aside.
In a big bowl, mix the all purpouse flour, cornmeal, sugar, salt, baking powder and baking soda. Make a holw in the middle of the flour and add the eggs, buttermilk, milk, honey, butter and oil. Stir with a spatula until there are only a few lumps remaining.
Pour the mixture in the previously greased pan and bake at 400°F (200°C) for 20-25 minutes until the top starts to turn golden brown. Servir caliente con un poco de mantequilla encima.