For the dressing: Put the bacon into a large nonstick skillet over medium heat and line a plate with paper towels. Cook the bacon, turning occasionally, until golden brown and crispy, 10 to 12 minutes. Transfer the bacon to the lined plate and transfer the bacon fat to a small mixing bowl. Add the mustard, sugar and vinegar to the warm fat and squeeze in the juice from the lemon half. Whisk to combine and season with black pepper. Set aside in a warm place.
For the potatoes: Preheat the grill over medium heat.
Place the potatoes in an even layer in a microwave-safe baking dish. Pour in 1/4 cup water and cover tightly with plastic wrap. Steam the potatoes in the microwave on high power until just slightly tender, about 3 minutes. Remove the potatoes and discard any water that remains.
Place the potatoes in a large mixing bowl with the whole scallions. Drizzle with the olive oil and sprinkle with the salt and pepper. Toss the vegetables to evenly coat in the oil.
Place the potatoes on the grill, cut-side down. Grill the potatoes until tender and caramelized, 7 minutes on each side. Meanwhile, place the scallions on the coolest area of the grill and cook, watching them closely to prevent charring, 1 to 2 minutes on each side. Remove the scallions from the grill and set aside. Remove the potatoes from the grill and place in a large mixing bowl.
Cut the grilled scallions into 1-inch pieces and place in the bowl with the potatoes. Crumble the cooked bacon into the bowl. Add the parsley and some sea salt and drizzle generously with the warm bacon dressing, then toss to coat.