Cover porcini mushrooms with 1/2 cup water in small microwave-safe bowl; cover bowl with plastic wrap, cut a few steam vents with paring knife, and microwave on high power for 30 seconds. Let stand until mushrooms have softened, about 5 minutes. Using fork, lift porcini from liquid and transfer to second small bowl; pour soaking liquid through paper towel-lined mesh strainer. Set porcini and strained liquid aside.
Bring wine to simmer in 10-inch nonstick skillet over medium heat; reduce heat to low and simmer until wine is reduced to 2 tablespoons, about 20 minutes. Set reduced wine aside.
Meanwhile, pulse carrot in food processor until broken down into rough 1/4-inch pieces, about 10 one-second pulses. Add onion; pulse until vegetables are broken down to 1/8-inch pieces, about 10 one-second pulses. Transfer vegetables to small bowl. Process softened porcini until well-ground, about 15 seconds, scraping down bowl if necessary. Transfer porcini to bowl with onions and carrots. Process pancetta until pieces are no larger than 1/4 inch, 30 to 35 seconds, scraping down bowl if necessary; transfer to small bowl. Pulse tomatoes with juice until chopped fine, 6 to 8 one-second pulses.
Heat butter in 12-inch skillet over medium-high heat; when foaming subsides, add pancetta and cook, stirring frequently, until well browned, about 2 minutes. Add carrot, onion, and porcini; cook, stirring frequently, until vegetables are softened but not browned, about 4 minutes. Add garlic and sugar; cook until fragrant, about 30 seconds. Add ground meats, breaking meat into 1-inch pieces with wooden spoon, about 1 minute. Add milk and stir to break meat into 1/2-inch bits; bring to simmer, reduce heat to medium, and continue to simmer, stirring to break up meat into small pieces, until most liquid has evaporated and meat begins to sizzle, 18 to 20 minutes. Stir in tomato paste and cook until combined, about 1 minute. Add tomatoes, reserved porcini soaking liquid, 1/4 teaspoon salt, and pepper; bring to simmer over medium-high heat, then reduce heat to medium and simmer until liquid is reduced and sauce is thickened but still moist, 12 to 15 minutes. Stir in reduced wine and simmer to blend flavors, about 5 minutes.
Meanwhile, bring 4 quarts water to rolling boil, covered, in stockpot. Add 1-tablespoon salt and pasta, stir to separate, and cook until al dente. Drain, reserving 1/4 cup pasta cooking water, and return pasta to stockpot. Add 2 cups sauce and 2 tablespoons pasta water to pasta; toss well, adding remaining pasta water, if necessary, to help distribute sauce. Divide pasta among individual bowls and top each portion with about 1/4 cup remaining sauce. Serve immediately, passing Parmesan separately.