Boil the pasta: Bring a large pot of generously salted water to a rolling boil. Add the tagliatelle and cook until 1 minute shy of al dente (about 10 minutes). Before draining, scoop out 1 full cup of the starchy cooking water and set it aside — this is the sauce's glue.
Sweat the aromatics: While the pasta cooks, heat the olive oil in a large skillet over medium heat. Add the diced onion and sliced garlic with a pinch of salt; cook 3-4 minutes until soft and sweet.
Brown the sausage meat: Slit the sausage skins with a knife and squeeze the meat directly into the pan. Break it up with a wooden spoon into small pieces. Cook 5-6 minutes over medium-high heat, stirring occasionally, until browned and crisp at the edges. Let it sit undisturbed for a minute or two between stirs — that contact with the pan is what builds the brown crust.
Add the tomatoes: Toss in the halved cherry tomatoes and the red-pepper flakes, if using. Season with salt and pepper. Cook 5 minutes over medium heat until the tomatoes slump and release their juices. Pour in 1/3 cup of the reserved pasta water and let it simmer into a loose, glossy sauce.
Marry the pasta and sauce (mantecatura): Drain the pasta and add it straight into the skillet. Toss everything together for 1-2 minutes over medium heat, loosening with more pasta water a splash at a time, until the sauce turns silky and clings to every ribbon.
Finish and serve: Take the pan off the heat, fold in the Parmesan until melted, and adjust the seasoning. Plate immediately with more Parmesan, torn basil and black pepper on top.