Melt butter and olive oil in a large flameproof casserole dish over low heat.
Seal gammon until golden on both sides for ten minutes and set aside.
Cook garlic, onions, and apple until translucent, then stir in flour for one minute.
Add cider, bring to a boil, and reduce the liquid by half.
Stir in piccalilli, honey, sage, and mustard, cooking for five minutes before seasoning.
Return gammon to the dish with lemon juice and stock.
Simmer covered for 20 to 30 minutes with extra seasoning.
Fill a pot with 2 liters of salted water and bring to a boil.
Boil potatoes, carrots, sugar, and garlic for 20 minutes until tender.
Drain and mash vegetables with olive oil, parsley, lemon juice, and seasoning.
Stir mash over low heat for 3 minutes.
Serve the carrot and potato mash with the glazed gammon.