Heat 1/4 cup of the olive oil in a large saute pan over medium-high heat until hot. Add the mushrooms and do not move them until they begin to brown, about 1 minute. Then saute until brown all over, about 5 minutes. Add another tablespoon olive oil if the pan is too dry. Season with salt and pepper, to taste.
Add the garlic and cook quickly until light brown. Add the thyme, fennel seeds, and stock and bring to a boil. Add the greens, season with salt and pepper, and simmer until tender, about 8 minutes.
Meanwhile, bring a large pot of water to a boil and add salt. Add the pasta and cook until al dente, about 12 minutes. Drain, refresh quickly under cool running water, and toss with the remaining 1 tablespoon olive oil.
Stir the butter into the greens and add the pasta and parsley. Toss to heat through and add half of the Parmesan. Toss well again and pour onto a heated serving platter. Dust with the other half of Parmesan and serve.