Set the oil, shallots and a pinch of salt in a large-skillet over moderate heat. Then cook, stirring often or till the shallots are softened, but not browned.
Add the mushrooms into the pan. Then cook the mushrooms for a couple minutes, till they take some color. Stir and add ½ tsp salt. Keep on cooking until the mushrooms become tender along with their liquid evaporates.
Meanwhile, bring a large-pot of water to a boil and add 2 tbsp kosher-salt. Cook the pasta till al dente, stir and reserve ½ cup of the pasta water, then drain the pasta.
Add the rosemary, garlic, chili, tomato paste, butter and vinegar into the mushrooms. Then add ⅓ cup of the pasta-water and stir over moderate heat or till the mixture saucy.
Add the pasta into the pan & toss gently with tongs to coat with the sauce, adding more water if it appears too dry. Taste for seasoning.
Serve and enjoy! Top with parmigiano-cheese over the pasta.