Cook pasta according to package directions, omitting salt and fat. Drain pasta in a colander over a bowl, reserving 2 tablespoons pasta water. Combined pasta, reserved pasta water, 1/4 cup cheese, 1 tablespoon oil, chopped basil, and pepper in a large bowl; toss well.
Heat remaining 1 tablespoon oil in a large cast-iron skillet over high heat. Sprinkle salt evenly over scallops; add scallops to pan. Cook 1 minute on each side or until golden.
Place 1 cup pasta mixture on each of 4 plates; top each serving with about 3 scallops and 1 1/2 teaspoons remaining cheese. Serve with lemon wedges.