Cook the tagliatelle pasta in a large pot of salted boiling water according to package instructions until al dente.
Meanwhile, place the dried porcini mushrooms in a small bowl and cover them with the hot water. Let them soak for 10-15 minutes.
In a large skillet, melt the butter and olive oil over medium heat.
Add the onion and garlic to the skillet and cook until softened, about 5-7 minutes.
Add the rehydrated porcini mushrooms and their soaking liquid to the skillet.
Increase the heat to high and cook until the liquid has evaporated and the mushrooms are lightly browned, about 5-7 minutes.
Add the white wine to the skillet and bring it to a simmer.
Reduce the heat to low and stir in the heavy cream and Parmesan cheese.
Cook the sauce, stirring frequently, until it has thickened and coats the back of a spoon, about 5-7 minutes.
Season the sauce with salt and pepper, to taste.
Drain the tagliatelle pasta and add it to the skillet with the mushroom sauce.
Toss everything together until the pasta is coated in the sauce.
Sprinkle chopped parsley over the pasta and serve hot.