Bring a large pot of lightly salted water to boil. Add pappardelle, and cook until al dente, 8 to 10 minutes. Drain, reserving some pasta water. Coat with 1 tablespoon olive oil; set aside.

Meanwhile, heat 1 tablespoon olive oil in a large non-stick skillet over medium high heat. Add zucchini; cook and stir until zucchini begins to brown around the edges but is still firm. Stir in asparagus, broccoli, and green beans; continue to cook until vegetables turn bright green in color, about 3 minutes. Add green onions and garbanzo beans; cook and stir until vegetables are lightly browned around the edges.

Add reserved pasta water to vegetables. Cover skillet; reduce heat to low and simmer until garbanzos are heated through and vegetables are just tender. Stir vegetables and basil into pasta; season to taste with salt and pepper, and top with crumbled feta.