I'm calling this a burger because all the other words I could think of just didn't sound quite right. Fritter sounded too small, although you could make them smaller, I wanted these big and chunky, like fishcakes from the chip shop. Patty just sounded neither here nor there and I felt like it wouldn't arouse much enthusiasm. You don't think "mmm I really fancy a patty for tea!" do you? I could have gone for 'bake' or 'cake' but it wouldn't have been clear what it was.
Perhaps burger is also unclear though. They are made of mashed potato so I'm not sure you would want to have one in a burger bun (although on days when I am craving a complete carb fest... never say never). But It gives the idea of something round in shape and really really delicious which I think these are. So for want of a better word, I'm calling them burgers. If anyone has any better suggestions, please feel free to comment.
I'm going to be really vague about the quantities here because its the kind of dish you are probably going to make with leftovers. I certainly did, so I will give ratios, rather than quantities because it depends how much of the ingredients you have available. It really doesn't matter too much about the quantities you use, as long as its seasoned well and served hot, it will be really good!

Ingredients:
1 part cooked ham/ gammon
1-1.5 parts mashed potato
4-6 tablespoons grated Parmesan (for 2-4 burgers, although if you are making a larger quantity, go large on the Parmesan, more is definitely more in this case!)
Roughly 1 cup of plain flour
1-2 eggs.
Olive oil for frying.
Method:
If you are using left over mashed potatoes they will probably already have seasoning and butter in them but if your making it fresh, first mash cooked potatoes with as much butter and seasoning as you usually would. Don't add too much milk or cream though as you want the mash to be stiff enough to form into burger shapes. The more butter you use here, the nicer it will be but I will leave that up to you.
Leave to cool and shred the ham. Add the shredded ham and half of the Parmesan to the potato and mix thoroughly.
Shape into fat burger- like round shapes and set aside.
lightly beat the egg in a shallow dish. I used 1 egg for the 4 burgers in the picture and it was just the right amount. If making more, use 2 eggs.
Put the cup of flour onto a plate and carefully season and mix in the remaining Parmesan.
Dip the burgers once in the egg to fully coat and then coat with the flour. You could use breadcrumbs here as well which would be really nice.
Shallow fry for about 3-4 mins on each side in a frying pan. If the sides need browning up a bit, carefully fry the sides as well.
Place in an oven proof dish and cook in a moderate oven for another 10 minutes. They should be golden and crispy on the outside and fluffy and piping hot on the inside.
I served these with baked, shredded sprouts and fennel and a dollop of spicy tomato chutney but they would be great with a fresh salad or slaw and probably really good with an egg for breakfast too!
The best thing about this dish is that its so cheap to make. I'm not going to work out the pence per serving as chefs usually do, because I always thing it doesn't really mean anything to anyone apart from chefs. (For example, you might only use 34p worth of Parmesan but to normal people, you either have to go out and buy it which means its actually costing you about £3-£4, or you have it in the fridge already which means it costs you £0. Does that make sense?)
What i mean by it being a cheap dish is that it will make a relatively small amount of leftover meat go a long way, which means you don't have to go out and buy anything else! Result!
BTW, if anyone tries this kind of 'burger' in a bun, please let me know what its like? I suspect that if you had it the day after a heavy night out drinking, it may be surprisingly satisfying, but under normal circumstances, not good! Would be interesting to find out. :)