Pour 2 cups of near-boiling water over the dried porcini mushrooms and leave to steep while you get on with the rest of the cooking. Peel the onions, carrots and garlic cloves and chop them; I use a food processor here, and do them in 2 batches of 2 each.
Pour the oil into a very large, thick-bottomed pan and when it's warm add the chopped onions, carrots and garlic. Cook, stirring, for about 10 minutes, sprinkling in salt if the vegetables look as though they might burn.
Drain the porcini, reserving the soaking liquid, chop them coarsely and add them to the vegetable mixture along with the button mushrooms. After about 5 minutes, when the fresh mushrooms have cooked down a bit into the mixture, transfer the vegetables to a plate so that you can start cooking the meat. Add a little more oil to the pan then add the minced meats, breaking them up with a wooden fork or spatula. Stir for about 5 minutes until the rawness has left them a bit, add salt liberally, and then return the vegetable mixture to the pan. Stir in the flour and, still stirring, pour in the mushroom-soaking liquid, tomatoes, tomato paste, Marsala and a few drops of Worcestershire sauce. Stir well, cover partly with a lid and turn down the heat so that the mixture bubbles gently with some of the liquid evaporating and the flavours intensifying, for about an hour. Even longer wouldn't do it any harm providing the heat is very low.
Once cooked, taste for seasoning then remove from heat. If it helps you can cook the base in advance (either freezing it or leaving it in the fridge for a few days), which means that when you want to serve the pie, you have only to bother with the topping. Some people are happy to make a shepherd's pie in its entirety and then leaving it to be reheated, but I think that's only OK if you don't need to refrigerate it for days (it does something funny to the texture of the potatoes). An afternoon, even a longer stretch, in a cold wintry kitchen, though, is fine. An easier alternative might be to refrigerate the cooked base and leave the mashed potatoes and parsnips in a plastic wrapped bowl in a cold place in the kitchen for however long you need, bringing the two together just before they go into the oven.
Given the amount of potatoes stipulated, I suggest you hand people a peeler if you have any around who ask if there's anything they can do to help. Or use a potato ricer, which means you don't need to peel them. Either way, boil the potatoes in a large pan of salted water until they are nearly tender and then add the parsnips which have been peeled and cut into chunks. Simmer until the potatoes and parsnips are cooked to easily mashable tenderness, but not to the point of disintegration, then drain them and let them dry slightly in the colander while you warm the milk and melt the butter in the heat of the pan that you cooked the potatoes in. Rice the potatoes and parsnips straight into this pan (or mash them) and then grate in some fresh nutmeg and add salt to taste.
Put the meat mixture into a large dish approximately 12 1/2 inches by 14 1/2 inches in size. Then dollop the potato mash on top, spreading with a spatula, taking care to seal the edges to prevent the meat below from bubbling up in the oven. Use a fork to draw lines over the top, then dot with butter and sprinkle with Worcestershire sauce. If you're cooking this straight away, in other words when everything's still warm, about 10 minutes in a 425 degree F oven should be enough to make it piping hot and golden and crisp on top. If cooking from cold, about an hour in a 375 degree F oven should do it.