Place potatoes in a large saucepan, cover by an inch with cold water, add 1 tablespoon of salt and bring to a boil over high heat. Cook until just cooked through but not soft, about 40 minutes depending on the size. When cool enough to handle, slice crosswise into 1/2-inch thick slices. Must be fork tender!
Preheat grill to high. Brush potatoes on both sides with canola oil and season with salt and pepper. Grill until lightly golden brown on both sides and just cooked through, about 1 1/2 minutes per side. Remove to a bowl. Brush green onions with the remaining canola oil and grill until slightly charred and softened, about 4 minutes. Remove and thinly slice. Add to the potatoes.
Whisk together the vinegars, mustard and honey in a bowl and season with salt and pepper. Slowly whisk in the olive oil until emulsified and taste for seasoning. Pour the dressing over the potatoes, add the parsley and gently toss to combine. Serve warm or at room temperature.