Peel the potatoes and cut into cubes. Add to a large saucepan. Cover with cold, salted water and bring to a simmer over medium heat. Cook for 20 minutes, or until soft.
Finely chop the spring onions and olives.
Drain the potatoes and mash with a potato masher, add some olive oil and the hot buttermilk, mash until fluffy. Add the lemon zest, spring onion, black olives, capers, and green pesto. Keep warm.
Heat a grill/pan over a medium heat, season the pork chops with olive oil, salt, and pepper.
Grill the meat on both sides until golden brown and cooked through. Remove from the heat and add the lemon juice over the pork chops.
Serve the pork chops with the mash potato and some extra pesto.