Wash and lightly scrub potatoes. Steam over a saucepan of simmering water for 15-20 minutes, until cooked. Toss in 1 tablespoon of olive oil and sprinkle with sea salt. Set aside and keep warm.
Meanwhile, split chicken fillets into two thin halves by slicing through centre then flatten between two sheets of plastic wrap. Place a slice each of ham and cheese on base of each fillet and top with remaining half, pressing down firmly. Dust with seasoned flour, brushing off excess. Dip in egg and coat thoroughly with breadcrumbs.
Heat remaining oil and butter in a large frying pan on medium-high. Cook chicken for 3 minutes each side (adjust heat so butter does not burn), until cooked through and golden brown. Place on four heated plates, pour over butter from pan, if you like, and serve with lemon wedges. Serve with steamed potatoes.