Bring a large pot of water to a boil for the pasta.
In a small saucepan, heat the stock and saffron over medium-low until just hot. Cover and keep warm.
In a large skillet, heat the olive oil, two turns of the pan, over medium-high. Add the pancetta; stir for a minute. Add the mushrooms. Cook, stirring often, until lightly browned, 4 to 5 minutes. Add the asparagus, peas, shallots and garlic; season with salt and pepper. Cook until the asparagus is tender, 3 to 4 minutes more. Add the wine; stir until almost evaporated. Add the saffron stock; swirl in the butter. Reduce the heat to low.
Salt the pasta water. Add the pasta; cook to al dente. Add a ladleful of the pasta water to the mushroom sauce, then drain the pasta. Toss the pasta with the sauce and herbs; season. Serve in shallow bowls, passing cheese alongside.