In a large bowl sift together the flour, sugar, baking powder and bicarbonate of soda. Whisk the eggs with the buttermilk and melted butter. Combine the dry and wet ingredients into a lumpy batter, being careful not to over mix.
Heat some butter in a pan over medium heat. Spoon some batter into the pan and sprinkle the top with some of the blueberries. Wait until bubbles that arise start to pop (about 30 seconds) and then carefully flip to cook on the other side.