Fill a large pot with at least 4 to 5 quarts of water and bring to a rolling boil over high heat. Season generously with salt until it tastes pleasantly salty, then keep the pot at a boil until ready to cook the pasta.
Remove sausage from casings, wipe mushrooms clean with a damp paper towel and slice into ½-inch pieces, finely dice the onion, mince the garlic, and crush the canned tomatoes by hand over a bowl. Measure out the white wine and heavy cream and set everything aside before you begin cooking.
Heat 1 tablespoon olive oil in a large deep skillet over medium-high heat, add the sausage meat, and cook for 5 to 6 minutes, breaking it into crumbles, until fully browned with no pink remaining. Transfer to a plate with a slotted spoon and set aside, leaving the rendered fat in the pan.
Add the remaining 1 tablespoon olive oil to the same skillet over medium-high heat, add the mushrooms in a single layer (in batches if needed), and cook undisturbed for 2 to 3 minutes before stirring. Continue cooking for another 3 to 4 minutes until golden brown and any released liquid has evaporated; season lightly with salt and pepper.
Reduce heat to medium, add the diced onion to the skillet, and cook for 4 to 5 minutes until softened and translucent. Stir in the minced garlic and cook for 60 seconds until fragrant, being careful not to let it brown.
Pour the white wine into the skillet and scrape up any browned bits from the bottom with a wooden spoon. Let the wine bubble and reduce by half, about 2 minutes, until the sharp alcohol smell has cooked off.
Add the crushed tomatoes with their juices to the skillet, return the browned sausage to the pan, and season with salt and pepper. Bring to a gentle simmer over medium-low heat and cook uncovered for 10 to 12 minutes, stirring occasionally, until the sauce thickens slightly.
Drop the pasta into the boiling salted water and cook for 2 minutes less than the package directions indicate. Before draining, scoop out about 1 cup of starchy pasta cooking water and set it aside, then drain the pasta.
Add the heavy cream to the simmering sauce and stir to combine. Cook for 1 to 2 minutes over medium heat until the cream is fully incorporated and the sauce looks smooth and slightly thickened.
Add the drained pasta directly to the skillet and toss with tongs to coat, adding reserved pasta water a splash at a time (starting with ¼ cup) until the sauce is glossy and clings to the pasta. Cook together over medium heat for 1 to 2 minutes, tossing continuously.
Remove from heat, add the freshly grated Parmigiano Reggiano, and toss to combine. Taste and adjust seasoning, then divide among warmed bowls and top with extra Parmigiano, fresh parsley, and a twist of black pepper. Serve immediately.