Peel the potatoes and chop into 2 inch chunks. Put in a large pan, cover with cold water and put on a medium heat. Bring to the boil and cook until the potatoes are completely soft.
Meanwhile, put the olive oil in another large pan. Cut the leftover ham into 1 inch chunks. Add to the pan and cook over a medium heat for 2-3 minutes.
Cut the mushrooms into 1 inch chunks and add to the pan. Cook for another 5 minutes, stirring regularly.
Stir in the flour. Add 200ml cold water and stir again.
Cut the broccoli into small florets. Add to the pan with the ham. Stir again. Allow the liquid to come to a simmer, then take off the heat. Stir in the double cream, mustard and thyme, then pour into a deep ovenproof dish.
When the potatoes are soft, drain them then tip back into the pan. Add the butter then mash until smooth. Pile the mash on top of the creamy ham filling, then smooth over with a fork so that all of the filling is covered.
Sprinkle the Parmesan over the top and put in the oven for 35-40 minutes until golden brown and bubbling.