In a large cast-iron or Dutch oven casserole over medium heat, heat some olive oil and then add the pancetta, porcini, garlic, onions and carrots. They should cook slow and lightly brown, about 20 minutes.
In another large casserole over medium heat, brown the meat slowly in olive oil until it is a nice even brown color. This process should take around 30 minutes and the mixture should be stirred frequently so it will not stick. Salt and pepper liberally. Then add the tomato paste and saute for 5 minutes.
When finished, deglaze the pot with the vegetables by adding 1 cup of the red wine. Next, add the vegetables and pancetta to the pot with the meat. Then add the remaining red wine to deglaze the pot. Scrape all the bits and pieces that might accumulate and reduce by half, about 10 minutes. Then add the chicken stock, milk, crushed tomatoes and cheese rinds and simmer very gently for 2 hours.
Remove the cheese rinds and discard. Let the sauce sit and cool down before using; it's even better the next day! Finish the sauce with the basil and thyme.
Boil 2 gallons of salted water and add the perciatelli pasta. Cook until al dente. Drain all but a 1/2 cup of water off of the pasta and put the pasta directly into the pot of bolognese sauce. Simmer for 2 minutes to incorporate the sauce into the pasta, adding the reserved pasta water as necessary. Finish with the ground Pecorino Romano, torn basil and a drizzle of extra-virgin olive oil on top. Bon appetit!