Cook pasta as directed on package. Drain, reserving pasta cooking water.
Meanwhile, heat oil in large skillet on medium-high; add anchovies. Stir until broken into fine pieces. Stir in garlic. Reduce heat to low. Stir in daikon sprouts and wine. Simmer.
Add some of the pasta cooking water. Cook until reduced.
Stir in pasta. Slowly add greens, except fava greens, stirring after each addition until slightly wilted. Add lemon zest and cheese. Mix gently.
