In a medium saucepan place the potatoes and cover with enough water to top by 1-inch. Place over high heat and bring to a boil. Cook until the potatoes just begin to soften, about 15 minutes. Remove from the heat, cool under running cold water and cut in half.
Preheat a grill to medium-low heat.
Brush the potatoes and onions with the olive oil and place on the grill. Cook without disturbing until the potatoes and onions are well marked by the grill, about 5 to 6 minutes, turn 90 degrees and cook an additional 5 to 6 minutes. Place the andouille on the grill and cook, turning occasionally until well caramelized and cooked through, about 12 minutes. Turn the onions and potatoes over and cook a final 5 to 6 minutes. Remove the potatoes, onions and andouille from the grill and allow to cool. Dice the potatoes, finely chop the onions and the andouille and place into a medium bowl. Combine the remaining ingredients and toss well to combine. Serve immediately or wrap with plastic wrap and keep warm until ready to serve.