In a food processor or blender, pulse the basil leaves until finely chopped. Add the pine nuts, cheese, garlic and lemon juice. Turn the machine back on and add 3/4 cup of the olive oil in a slow, steady stream. Season the pesto with salt and pepper. Place the pesto in a bowl and cover with plastic wrap.
In a small bowl, combine the tomato and shredded basil and set aside. In a large skillet, heat the remaining 1 tablespoon of olive oil over medium-high heat until almost smoking. Add the scallops and sear until golden brown, about 2 minutes per side. Transfer the scallops to a plate. Drizzle 2 teaspoons of the pesto on each scallop and arrange the tomato and basil around the scallops. Serve immediately.