Rinse potatoes and place in a medium-sized pot. Fill with cold water to cover the potatoes. Place over medium heat and bring to a boil, reduce to medium-low and simmer until potatoes are fully cooked about 20 minutes. When pierced with a fork there will be no resistance. Drain potatoes. Set aside and let cool to the touch.
In a medium bowl whisk together the vinegar, garlic, olive oil, Dijon, sugar, salt, pepper, and pesto until combined.
Cut potatoes in half lengthwise. Add potatoes to the bowl with the marinade. Toss to coat.
Grill potatoes over high heat until grill marks form. This is a fast process so watch closely. If you find the potatoes are too small for the grill, you can skewer them ahead of time.
Once potatoes are grilled, place them back into the bowl with the marinade and toss to coat in any additional marinade that is left. Add butter and toss to coat. Taste, adjust seasoning if needed.