Put the potatoes in a pot and cover by 2 inches with cold water. Add 2 tablespoons of salt, bring to a boil and cook until a skewer inserted in the center of a potato meets no resistance, about 20 minutes. Drain well and cool slightly.
Preheat a grill to high heat. Halve the potatoes and toss with the canola oil, smoked paprika and some salt and pepper. Grill the potatoes cut-side down until golden brown and crusty, 4 to 5 minutes.
While the potatoes are grilling, whisk the vinegar, mustard, parsley and salt and pepper until combined. Slowly whisk in the olive oil. Taste; add a drop or two of honey if desired.
Mound the cooked and still warm potatoes in a large shallow bowl. Drizzle with the vinaigrette and top with the Parmesan and parsley leaves.
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