In a mixing bowl, combine the eggs, flour, baking powder, and olive oil. Whisk together while gradually adding the milk. Season with salt and pepper, and let the batter rest for 30 minutes.
Heat the olive oil in a small saucepan. Add the cornflour and cook for 2 minutes, stirring constantly. Gradually add the milk in two batches, stirring continuously until smooth. Season with salt and pepper, then set aside.