Bring a large pot of water to boil for the pasta.
In a large skillet, heat the oil over medium. Add the butter. When the butter foams, add the mushrooms and cook, stirring often, until browned, about 3 minutes. Add the asparagus, zucchini, shallots, garlic and lemon zest; season with salt and white pepper. Cook, tossing occasionally, until vegetables are crisp-tender, 3 to 4 minutes. Sprinkle with the flour; toss to coat, about 1 minute. Add the wine and cook, stirring often, until evaporated, about 2 minutes. Add the stock and bring to a bubble. Add the cream; return to a bubble. Reduce the heat to low and let the sauce simmer while the pasta cooks.
Salt the boiling water. Add the pasta; cook to al dente.
When the pasta is almost done, add the peas and a ladleful of pasta water to the sauce. Drain the pasta. Off the heat, stir the lemon juice into the sauce. Add the pasta and tarragon; toss to coat. Sprinkle the pasta with mint and parsley.