Preheat your grill to high heat. At the same time, bring a large pot of water to a rolling boil.

Slice the potatoes into wedges, adding them to the boiling water. Generally, cut russet potatoes into 8 wedges each and Yukon Golds into 4 wedges each.

Partially cook the potato wedges until a fork easily pierces them, which should take about 10 minutes.

In a medium bowl, whisk together the mayonnaise, Dijon mustard, lemon juice, and vinegar. Gradually whisk in the olive oil until the mixture is smooth and well combined. Season with salt and pepper to taste, then refrigerate until the potatoes are ready.

Drain the potatoes and brush them with canola oil. Season with kosher salt and freshly ground black pepper.

Place the potato wedges on the grill with one of the cut sides facing down. Grill with the lid closed for 2-3 minutes. Open the lid, flip the potatoes to the other cut side, and grill with the lid closed for another 2-3 minutes.

Remove the potatoes from the grill, sprinkle with smoked paprika, and coat with the prepared sauce. Garnish with chopped parsley.

Serve immediately.