To make the sauce, trim off the stem ends of the mushrooms, and cut the mushrooms in half. In a large frying pan, melt the butter over high heat. Add the mushrooms and shallots and cook, stirring occasionally, until the mushrooms and shallots begin to soften, 2 to 3 minutes. Add the asparagus and stock and simmer until the asparagus is almost tender and the stock has reduced by half, 3 to 4 minutes. Add the peas and cook, stirring occasionally, just until tender, 2 to 3 minutes. Add the crème fraîche and thyme, stir well, and heat for 1 minute. Season with salt and pepper.
Meanwhile, bring a large pot of water to a boil and salt generously. Add the pasta, stir well, and cook until al dente, about 3-4 minutes.
Drain the pasta, add it to the frying pan, and toss and stir with the sauce, mixing well. Transfer to a warmed serving dish and top with the parsley.