Melt the butter with the olive oil in a large casserole dish over low heat.
Sear the gammon steaks until golden on both sides and set aside.
Sauté the garlic, onion, and apple until the onion is translucent, then stir in the flour for one minute.
Pour in the cider, boil until reduced by half, then mix in piccalilli, honey, sage, and mustard.
Return the gammon to the dish with lemon juice and stock, then simmer covered for 30 minutes.
Bring a pot with 2 liters of salted water to a boil.
Boil the potatoes, carrots, sugar, and garlic for 20 minutes until tender.
Drain the vegetables and mash with olive oil, parsley, lemon juice, and seasoning.
Reheat the mash briefly for 3 minutes and serve with the gammon.