Toss the greens, salt and pepper together with just enough vinaigrette to coat, about 1/2 cup. Place them in a decorative bowl and top with the grape tomatoes and bell pepper. Serve the remaining vinaigrette on the side.
Put the shallot and basil into the bowl of a food processor fitted with a metal blade. Pulse until the shallot is finely chopped. Add the balsamic, sugar, salt and pepper and pulse again. With the machine running, add the olive oil in a steady stream through the feed tube. Pour the vinaigrette into a small bowl and serve.