Use a balloon whisk or electric beater to mix together the buttermilk or yoghurt with the eggs, oil and vanilla essence. Gradually whisk in the sugar, cornmeal, flour and baking powder to make a smooth batter. Spoon into the prepared muffin tins. Divide the blueberries or cranberries between them gently pressing the fruit into the mixture.
Bake in the preheated oven until the centres of the muffins are springy to the touch. Remove from the oven and serve straight away.