In a large skillet set over moderate heat 2 tablespoons of the butter and the oil until hot, add the shallot and cook, stirring, 3 minutes, or until softened. Add the mushrooms, thyme and salt and pepper to taste and cook the mixture, stirring occasionally, for 7 minutes, or until mushrooms are lightly golden. Add the prosciutto and peas and cook for 1 to 2 minutes, or until heated through. Add the cream and simmer just until lightly thickened.In a large pot of boiling salted water add the tagliatelle and cook it until al dente. Drain the pasta and transfer it to a serving bowl. Add the remaining butter to the pasta and toss to combine. Add the sauce and toss to coat the pasta. Serve with the Parmesan.