Toss together the cut potatoes with the oil, salt and pepper. Place in a single layer on a hot grill, flipping each after 4-6 minutes.

Zest lemon and place in a large bowl. Cut lemon in half and brush cut ends with a bit of oil and place cut-side down onto the hot grill. Grill for about 6 minutes, until nicely charred. Set aside until cool enough to handle.

Add remaining dressing ingredients to bowl. Juice the grilled lemons and pour into bowl (should have about 2 Tbsp). Whisk together to combine.

Once potatoes are grilled on both sides and tender, place into bowl with dressing and toss to combine. Allow them to sit at room temperature for at least 15 minutes before serving, the warm potatoes will soak up some of the dressing.

Serve warm or at room temperature.