Whisk oil, lemon zest and juice, garlic, and 1/2 teaspoon salt together in small bowl, then stir in Parmesan until thick and creamy. Set aside.
Melt 2 tablespoons butter in 12-inch nonstick skillet over medium heat. Pat scallops dry with paper towels and season with salt and pepper. Add scallops in single layer (uncovered) and cook until scallops are firm, about 3 minutes; transfer to bowl and cover.
Meanwhile, bring 4 quarts water to boil in large pot. Add pasta and 1 tablespoon salt and cook, stirring often, until al dente. Reserve 1/2 cup cooking water, then drain pasta and return pasta to the pot. Stir in reserved olive oil mixture, scallops with any accumulated juices, remaining 2 tablespoons butter and basil; toss to combine. Add reserved cooking water as needed to adjust consistency. Season with salt and pepper to taste.
Garnish with additional sprigs of basil, if desired.