In a small heatproof bowl or measuring cup, combine dried porcini mushrooms with white wine and microwave until wine is steaming-hot. Alternatively, heat wine and mushrooms in a small saucepan until steaming. Set aside and let soak until porcini are fully softened, 10 minutes. Using your hands, lift porcini from wine and squeeze well to remove any excess liquid; reserve porcini-infused wine. Chop soaked porcini coarsely.

Meanwhile, in a Dutch oven or large sauté pan, cook bacon over medium-high heat, stirring often, until browned, about 5 minutes. Using a slotted spoon, transfer bacon to a plate.

Add fresh mushrooms and chopped porcini to pot with rendered bacon fat and return to medium-high heat. Cook, stirring often, until mushrooms are browned, about 8 minutes. Add a splash of olive oil at any point if pot becomes too dry.

Add onion, garlic, and thyme and cook, stirring, until onion and garlic are softened and lightly golden, about 6 minutes; again, add olive oil as needed if pot becomes too dry. Season with salt and pepper.

Add bacon back to pot, then add crushed or puréed tomatoes. Pour in porcini-infused wine through a fine-mesh strainer to remove any sediment. Bring to a simmer, then lower heat to maintain a bare simmer. Season with salt.

Meanwhile, bring a pot of salted water to a boil. Add pasta and cook until just shy of al dente. Drain pasta, reserving about 2 cups of pasta-cooking water.

Add cream to pasta sauce along with drained pasta. Bring to a simmer, adding reserved pasta-cooking water as needed to thin sauce, until pasta is al dente and sauce forms a creamy sheen that coats pasta. If sauce ever becomes too thick, add more pasta water to thin it out. Remove pasta and sauce from heat and stir in parsley and cheese. Serve, passing more cheese at the table.