Soak mushrooms in warm water 30 minutes; drain, reserving liquid. Chop mushrooms (you should have 1/3 cup). Melt butter in a Dutch oven or a large, heavy straight-sided skillet over medium-high heat. Add pancetta; cook, stirring, until browned and crisp, about 1 minute. Add onion, carrot, celery, and garlic. Season with 1 teaspoon salt and 1/2 teaspoon pepper; cook, stirring occasionally, until vegetables are softened and beginning to brown, about 6 minutes. Transfer to a bowl.

Add 2 tablespoons oil to Dutch oven; heat until shimmering. Add both meats, increase heat to high, and cook, stirring occasionally, until browned, 3 to 4 minutes. Return vegetables to Dutch oven with marjoram, nutmeg, parsley, and basil. Add Marsala and bring to a boil; cook, scraping up browned bits, until liquid has almost evaporated, about 1 minute. Add 1/2 cup mushroom liquid and mushrooms, broth, and tomatoes. Bring to a boil, then reduce heat to low, cover, and simmer, stirring occasionally, 1 hour. Stir in cream and cook, uncovered, stirring occasionally, until reduced and thickened, 20 to 25 minutes more.

Meanwhile, bring a large pot of salted water to a boil. Add pasta to boiling water and cook until floating and tender, about 1 minute. Reserve 1 cup pasta water, then drain. Transfer pasta to skillet with sauce. Add 1/2 cup pasta water; toss to combine and finish cooking, about 30 seconds. Remove from heat; add cheese and remaining 1/4 cup oil. Serve with more cheese, oil, pepper, and basil leaves, if desired.