Heat the butter over medium-high heat in a large pan.
Add the onion, garlic celery and carrots and cook gently for 5 to 9 minutes, stirring often. Do not brown them. Sprinkle a little salt over the onions to prevent them from burning.
Stir in the chopped porcini mushrooms and tomato paste and allow everything to cook for 4 or 5 minutes, again, stirring often. When the tomato paste begins to turn a rusty red color, add the ground meat, the porcini soaking water and the broth. Bring to a simmer.
Allow the sauce to cook down over low heat. Stir from time to time.
When the liquid has mostly evaporated, add the wine and chopped tomatoes and cook down again over a low heat. Stir from time to time.
Add the milk, nutmeg and black pepper and stir well.
Bring back to a simmer and add salt to taste. Let this cook until it is the consistency you want.
Cook pasta al dente and add two ladles of sauce to the pasta. Combine well.
Serve the pasta on deep plates and top with a small ladle of sauce.