Bring a large pot of salted water to a boil. Add the gnocchi and cook as the label directs. Reserve 1 cup cooking water, then drain.
Meanwhile, heat the olive oil in a large skillet over medium-high heat. Add the leek and cook, stirring occasionally, until it softens and just starts browning, about 3 minutes. Add the radishes, sugar snap peas, 1/2 teaspoon salt and a few grinds of pepper. Cook, stirring often, until the peas are bright green and crisp-tender, 5 to 6 minutes.
Add the gnocchi to the skillet along with 3/4 cup of the reserved cooking water, the butter, grated parmesan, lemon zest and parsley. Remove from the heat and gently stir until the gnocchi are well coated and the cheese melts, adding more cooking water as needed to loosen. Top each serving with shaved parmesan.