Cut enough of scallion greens into 2-inch pieces to measure 3 cups and finely chop white parts. Mince garlic. Shell and devein shrimp.
Fill a 6-quart pasta pot three fourths full with salted water and bring to a boil for scallion greens and pasta.
In a deep 12-inch heavy skillet cook finely chopped scallions in 2 tablespoons oil over moderately low heat, stirring, until tender, about 5 minutes. Add garlic and cook, stirring, 1 minute. Transfer mixture to a blender and wipe skillet clean.
Blanch scallion greens in boiling water 30 seconds and with a slotted spoon transfer to blender. Transfer 1/4 cup scallion water to blender and reserve water remaining in pot over low heat, covered. Blend scallion mixture with 2 tablespoons oil until smooth (use caution when blending hot liquids). Season sauce with salt and pepper.
In skillet heat 2 tablespoons oil over moderately high heat until hot but not smoking and sauté half of shrimp, turning them, until golden brown on both sides and just cooked through, about 2 minutes. Transfer shrimp to a plate and keep warm, covered. Sauté remaining shrimp in same manner, adding remaining tablespoon oil if necessary, and keep warm in skillet, covered.
Return water in pot to a boil. Cook pasta in boiling water, stirring occasionally, until al dente and ladle out and reserve 1 cup pasta water. Drain pasta in a colander and add to skillet with sauce and 1/4 cup reserved pasta water. Heat mixture over low heat, gently tossing (and adding more pasta water as needed if mixture becomes dry), until just heated through. Serve pasta topped with remaining shrimp and garnished with scallion greens.