Soak the dried mushrooms in hot water until they're pliable and easy to cut with a knife, about 20 minutes.

Heat the olive oil in a large, deep saute pan or dutch oven over medium, until it shimmers. Add the chopped bacon and cook until the fat begins to render. Stir in the onions, celery, and carrots and continue sauteing until soft and the onions are translucent. Pour in the wine, allowing most of the liquid to evaporate before continuing.

Remove the re-hydrated mushrooms from the water — reserve the liquid — rinse and blot with a paper towel. Chop into 1/2" pieces and add to the cooking vegetables, along with the cremini, shiitakes and a big pinch of salt. Cover the pan with a lid and steam until the mushrooms have exuded their liquids and are dark and soft (about 5 to 8 minutes). Stir in the tomato paste and mix well.

Add the crushed tomatoes and fish sauce/Worcestershire sauce (if using) to the pan. Reduce heat to a simmer and partially cover with the lid. Let the sauce do its thing for about a 1/2 hour — the sauce should be thick and rich. Thin just a bit with the reserved mushroom water for an added touch of mushroom flavor. Taste, seasoning with salt and pepper as needed. Turn the heat to low and allow to rest for 5 minutes.

Gently stir in the dairy until completely incorporated into the sauce. Finish with a big palmful of shredded cheese, stirring until it melts and disappears. Serve over pasta or tortellini; top with remaining cheese.