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