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.
This is without a doubt the best salad I've ever had or made! Everyone who tastes it raves about it and wants the recipe. I use tiny red, white and blue potatoes, more basil and more cheese (crumbled) and only about a handful of arugula.
I used corn since fresh isn't locally available yet. I left out the cheese altogether so my vegan sister could eat this, and since I was also serving a mixed greens tossed salad didn't add arugula either. Excellent switch from routine potato salad, and beautiful to look at. Went well with steamed lobsters and steaks for the 4th. Everyone liked it. Will definitely make again.