Cook spaghetti in a 6- to 8-quart pot of boiling salted water until al dente.
While pasta cooks, heat 3 tablespoons olive oil in a 12-inch heavy skillet over moderate heat until hot but not smoking, then cook scallions and garlic, stirring occasionally, until scallions are softened and garlic begins to turn golden, about 5 minutes.
Transfer scallion mixture to a blender and add zest, salt, pepper, remaining olive oil, and 1/2 cup pasta-cooking water, then purée until smooth. (Use caution when blending hot liquids.)
Drain pasta in a colander and return to pot.
Toss pasta with scallion purée, cheese, and salt and pepper to taste over moderate heat until pasta is well coated.
