Place potatoes in a small saucepan; cover with water. Bring to a boil; cook 11 minutes or until tender. Drain and chill. Cut potatoes in half lengthwise. Combine potatoes, corn, tomatoes, and bell pepper in a large bowl.
Combine shallots and next 4 ingredients (through black pepper) in a small bowl, stirring with a whisk. Slowly pour oil into shallot mixture, stirring constantly with a whisk. Drizzle over corn mixture; toss well. Add arugula; toss. Sprinkle with basil; top evenly with goat cheese.