In a blender container combine undrained tomatoes, vinegar, and brown sugar. Cover and blend until smooth. With blender running, gradually add oil in a steady stream. Cover and let stand 20 minutes to blend flavors or chill up to 4 days. If chilled, let stand at room temperature for 30 minutes before serving. Stir before serving.
Meanwhile, in a salad bowl toss together spinach, arugula, endive, radishes, if using, and basil. Add 1/4 cup dressing; toss to coat. Top with Parmesan cheese; pass remaining vinaigrette. Makes 8 servings.