Prepare an ice-water bath. Cook green and wax beans in a large pot of boiling salted water until tender, about 4 minutes. Using a slotted spoon, transfer beans to ice-water bath until cool, reserving water in pot. Drain beans, and cut into 2-inch-long pieces.
Add pasta to the reserved boiling water, and cook until al dente. Drain and spread on a rimmed baking sheet. Refrigerate for 10 minutes. Transfer chilled pasta to a large serving dish.
Whisk lemon zest and juice and 3/4 teaspoon salt. Season with pepper. Add oil in a slow, steady stream, whisking until emulsified. Drizzle over pasta, and toss until well coated.
Add beans, pine nuts, and grated Parmesan. Toss until evenly distributed. Just before serving, fold in arugula, and top with shaved Parmesan.