Put the potatoes in a pot of salted water and bring to a boil over high heat. Boil until potatoes are just tender, about 8 min.
Drain and cool slightly, then cut potatoes in half or quarters.
Heat grill to medium-high.
Toss the potatoes with canola oil and season with salt and pepper.
Put the potatoes in a grill basket and grill, covered, tossing, and turning, until lightly charred about 5 min.
Transfer the potatoes to a bowl and immediately add the vinaigrette.
Put the arugula on top and scatter the goat cheese over the arugula.
Season with salt and pepper.
Quickly and gently fold the mixture once or twice to combine.
Serve warm or at room temperature.