Bring 3 quarts of well-salted water to a boil in a large pot over high heat.
Meanwhile, heat the oil in a 10-inch straight-sided sauté pan over low heat. Add the green garlic and 2 big pinches of salt; stir to coat. Cover and cook, stirring frequently, until wilted and softened, 5 to 7 minutes. Remove the pan from the heat.
Boil the spaghetti until just al dente, about 1 minute less than package timing. Set aside about 1/2 cup of the cooking water and drain the pasta.
Return the sauté pan to low heat. Add the spaghetti and 1/4 cup of the cooking water; toss well. Add the Parmigiano and 2 Tbs. of the water; toss again. Season to taste with salt and pepper, adding the remaining water if the pasta seems dry. Serve in heated pasta bowls, sprinkled with additional Parmigiano.
nutrition information (per serving):
Photo: Scott Phillips