Wash the scallops. Remove the tough tendon on the side and dry well on paper towels. In a large saucepan or flame-proof casserole, heat the oil. Add the garlic and cook over moderately low heat until softened but not browned, about 3 minutes. Add the pine nuts, increase the heat to moderate and cook, stirring frequently, until the nuts are lightly browned, about 2 minutes. Remove the sauce from the heat and season with 1/2 tsp. of the salt and all of the pepper.
Bring a large pot of water to a boil. Add the remaining 2 tablespoons salt and the spaghettini. Cook the pasta until al dente, 8 to 10 minutes.
Meanwhile, add the scallops to the garlic and pine nut sauce. Cook over high heat, tossing frequently, until the scallops are just opaque throughout, 2 to 3 minutes. Remove from the heat and season with an additional pinch of salt and pepper.
Drain the spaghettini, add to the scallops and toss. Add the butter and basil and toss again. Serve hot. Makes 6 to 8 servings.