Put the flour, bicarbonate of soda, cream of tartar and sugar in a bowl and make a well in the centre. Add the eggs, oil and half of the milk to the well, and gradually incorporate the flour with a whisk. Add the remaining milk and whisk well to make a smooth batter.
Melt a small knob of butter in a large non-stick frying pan. Cook the scones in batches. Drop large spoonfuls of batter into the pan from the tip of the spoon to form rounds, spacing well apart. Cook for 2 to 3 minutes until bubbles appear on the surface and burst, then turn them over and cook for a further 1 to 2 minutes until golden brown underneath. Put the scones on a clean tea and fold it over to keep them warm, while cooking the rest of them.
Serve the scones warm, either plain or topped with a spoonful of the blueberry compote and a dollop of yoghurt.