Bring water to a boil and salt it liberally, drop in pasta and cook to al dente.
While pasta cooks, heat olive oil, 3 turns of the pan, over medium heat. Add mushrooms, celery, shallots and garlic, cook 4 to 5 minutes then add tomatoes, season with salt and pepper, raise heat to medium-high and cook tomatoes until they burst, 4 to 5 minutes. Stir in peas and crab, heat through 2 minutes then add hot sauce and wine, reduce wine a minute then stir in stock, heat 1 minute more then add cream - a turn of the pan, parsley, tarragon. Adjust seasonings. Drain pasta and toss with sauce, sprinkle with cheese to taste, optional.