If the ham is very salty, either soak in cold water overnight before draining and cooking, or put the ham in a large pan, cover with water, bring to the boil, and then drain and cook as follows. Otherwise — and mild cure ham probably needs neither of those treatments — put the ham in a large pot, add the 2 quartered carrots, the onions, the green end parts of the leeks (as long as they're not muddy), peppercorns, celery, parsley (if you keep the stalks together with a freezer bag wire it'll be easier to remove them later) and bouquet garni. Pour in the cider: I never mind which cider I use and I have profitably used apple juice, too. Then add cold water to cover and bring to boiling point.
Add the sugar, lower the heat and simmer briskly (or boil gently, depending on how you want to look at it) for about 1 hour 50 minutes. (And at about this stage you should start thinking about the potatoes, see below). Remove the carrots, green parts of leek and parsley, and put in the fresh carrots. After about another ½ hour, chop up the white bits of the leek. I would cut them into logs about 6 cm long. Add to the pan and cook for about another 20 minutes. The ham should be bubbling softly in its liquid for around 2 ½ hours, all told. When it's all cooked, remove the ham to carve it, take the vegetables out with a slotted spoon and then put the ham on a huge plate surrounded by the leeks and carrots. Or carve it to order at the table and put the vegetables on a plate on the table by themselves.
Now: the potatoes. You can do either of two things: You can boil the potatoes in a pan of water while the ham is cooking, or you can cook them in the ham water itself. The advantage of cooking them separately is that they offer a distinct, appropriately plain taste. And potatoes are really at their best when they are the bland but sweet bass note to sop up and support other, stronger tastes. Added to which, you are left with a clear stock at the end; if you cook the potatoes in with the ham, all you can do with the stock, really, is make thick soup. And unless you have a very big pot, the ham, vegetables and potatoes all in together will be a very tight squeeze.
Having said that, there is something wonderful about the sweet, grainy potatoes absorbing all that appley and salty stock. You decide. But whichever way you cook the potatoes, they should be the big, floury sort, not the pebbly, waxy ones. I reckon on 1 potato (cut into 4) per person; I might even do 1 ½ per person, but then I like to have too much rather than not enough.
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