Place a large flameproof casserole dish on a low heat and gently melt the butter with the olive oil.
Add the gammon steaks and seal until golden on both sides (about 10 minutes). Remove the gammon and place to one side.
Now add the garlic, onion and apple to the casserole and cook until the onion is translucent. Add the flour and cook for one minute.
Add the cider, bring to boil and reduce by half. Then add the piccalilli, honey, sage leaves and mustard, and cook for five minutes. Season.
Now put the gammon steaks back into the casserole, squeeze in the lemon juice and pour in the stock. Add another good pinch of salt and pepper, cover and simmer for a further 20-30 minutes.
For the mash, half-fill a pot with water (about 2 litres/3 pints 10fl oz), add salt, cover and bring to the boil.
Add the potatoes and carrots to the boiling water, together with the sugar and garlic. Boil for 20 minutes on a moderate heat until the vegetables are tender.
Drain and mash vigorously, mixing in the olive oil, chopped parsley, a squeeze of lemon juice, and seasoning to taste.
Return to a low heat and stir gently for 2-3 minutes. Serve the mash with the gammon.