Step 1Heat the broiler. Melt the butter in a 10-inch nonstick skillet over medium low heat. Add the green onions and cook until they've softened slightly, about 2 minutes. Add the shrimp and cook until they are firm, about 5 minutes.
Step 2While the onions and shrimp are cooking, beat the eggs, salt and basil with a fork in a mixing bowl just until the yolks and the white are thoroughly mixed, but don't overbeat, which can make the frittata dry.
Step 3Add the egg mixture to the pan with the onions and shrimp and stir well to combine. Reduce the heat to low and cover the pan. Cook, without stirring, until the eggs have set, leaving only a top layer uncooked, about 10 minutes. Place under the broiler until the top is browned and puffy, 1 to 2 minutes.
Step 4To unmold the frittata, let it cool slightly in the pan. Use a spatula to loosen it along the sides, and then bang it firmly on a cutting board to release the underside. Slide it out onto a serving plate. Serve either hot or at room temperature. If you're going to refrigerate the frittata, let it warm to room temperature before serving.