Line a plate with paper towels and set aside.
Place the potatoes in a medium saucepan and cover by about 2 inches with cold water. Add salt and bring to a boil over medium-high heat. Boil gently until the potatoes are tender enough to pierce easily with a knife, about 15 minutes. Don’t overcook them or they will fall apart.
(You can also microwave them until tender. Place the potatoes in a microwave-safe covered dish and season with salt and pepper. Cover and cook on high until just tender, about 8 minutes depending on the strength of your microwave.)
Drain the potatoes in a large colander and let cool. Meanwhile, cook the bacon in a large skillet over medium heat, stirring occasionally, until crisp, about 5 to 7 minutes. Drain on the prepared plate.
Remove all but about 2 teaspoons of the bacon drippings from the pan. Add garlic, vinegar, and brown sugar to the drippings, scraping up any browned bits. Whisk in 2 tablespoons of the oil and season with salt and pepper. Set aside.
Prepare a charcoal fire using about 6 pounds of charcoal and burn until the coals are completely covered with a thin coating of light gray ash, 20 to 30 minutes. Spread the coals evenly over the grill bottom, position the grill rack above the coals, and heat until medium-hot (when you can hold your hand 5 inches above the grill surface for no longer than 3 or 4 seconds). Or, for a gas grill, turn all burners to high, close the lid, and heat until very hot, 10 to 15 minutes.
Working in batches, grill the potatoes cut-side down on the grill until they have developed a light char, 2 to 3 minutes.
Grill the onions until they are charred, 4 to 6 minutes a side. Chop the green onions into 1-inch pieces and add to the bowl with the potatoes.
Add the reserved bacon vinaigrette and parsley. Toss to coat. Let all sit for a few minutes to allow the flavor to penetrate the potatoes. Sprinkle with reserved bacon and toss to coat. Taste and adjust for seasoning with salt and pepper. Serve immediately.