Pour the oil into a large pan and warm it over medium heat. Add the onion and garlic, then cook gently, stirring occasionally, for 3–5 minutes until they become soft and translucent without taking on any color. Toss in the mushrooms, increase the heat to high, and stir-fry for approximately 5 minutes until they release their moisture and begin to brown.
Add the tomatoes to the pan and season the mixture generously with salt and pepper. Let it simmer gently, leaving the pan uncovered, for about 20 minutes. Stir occasionally as the sauce reduces and thickens to a rich, concentrated consistency.
While the sauce is simmering, bring a large saucepan of salted water to a rolling boil. Add the tagliatelle and cook for 8–10 minutes, or according to the package directions, until the pasta is just tender with a slight bite (al dente).
Stir the shrimp and crème fraîche into the thickened tomato sauce, folding them in gently. Cook over low heat for about 2 minutes, just until the shrimp is warmed through and the cream is incorporated. Taste the sauce and adjust the seasoning if needed.
Drain the cooked tagliatelle thoroughly in a colander, shaking off any excess water, then divide it among warmed serving plates, creating neat piles or nests. Ladle the creamy shrimp and tomato mixture generously over the top of each portion. Finish with a sprinkle of fresh chopped parsley for color and serve immediately while everything is hot.
