Reconstitute the mushrooms in boiling water for 20 minutes until tender, drain and coarsely chop.
In a large heavy-bottomed saucepan, heat the olive oil over medium flame. Add the pancetta and saute for 2 minutes to render out the fat. Add the porcinis, onion, celery, carrots, and garlic; stirring to combine. Toss in the thyme, oregano, rosemary, and bay leaves. Cook for 5 to 10 minutes, stirring, until the vegetables are very tender but not browned.
Raise the heat a bit and add the ground pork and beef; brown until the meat is no longer pink, breaking up the clumps with a wooden spoon. Add the milk and simmer until the liquid is evaporated, about 10 minutes. Carefully pour in the tomatoes and wine; season with salt and pepper. Bring the sauce to a boil, then lower the heat and cover. Slowly simmer for 1 1/2 to 2 hours, stirring now and then, until the sauce is very thick. Taste again for salt and pepper.
When you are ready to serve, bring a large pot of salted water to a boil, add the pasta and cook for 8 to 10 minutes or until tender yet firm (as they say in Italian "al dente.") Drain the pasta well and toss with the Bolognese sauce. Shower with basil and pass grated cheese around the table.