Blend all the ingredients except the cheese into a consistent paste, then stir in the cheese and set aside.
For the scones
Preheat the oven to 180C/350F/gas 4.
Mash the eggs into the potato with a fork, then sift in the flour baking powder and salt. Mash roughly, then add 150g/5 oz of the pesto and bring it all together to a dough. Reshape the dough and continue cutting out the scones. Bake for 20-25 minutes until risen and slightly browned. Remove from the oven and cool on a wire rack for 5-10 minutes.
Tip the dough out onto a floured surface and flatten to around 3cm/1 1/4 in thick. Punch out the scones using cookie cutter and place on the floured tray.
Reshape the dough and continue cutting out the scones. Bake for 20-25 minutes until risen and slightly browned.
Remove from the oven and cool on a wire rack for 5-10 minutes.
Notes
Serve warm, slathered with cold butter. I rolled my scones more thinly than the recipe suggests to make them more like traditional Scottish Tattie Scones, but if you cut them thicker then they will be more like the more usual scones.