Prepare a medium-high (425°F to 450°F) gas or charcoal grill fire. Brush the pepper quarters with oil and season with salt and pepper.
Put the potatoes in a 4-quart pot with 1 tsp. kosher salt and enough cool water to cover. Boil over high heat, partially covered, until just tender, about 8 minutes. Drain and transfer to a large bowl.
Meanwhile, grill the peppers skin-side down until grill marks form on one side, about 5 minutes. Flip the peppers and continue to grill until crisp-tender, about 2 minutes more. Let the peppers cool slightly, then cut into bite-size pieces and add to the potatoes.
In a small bowl, combine the mayonnaise, parsley, and garlic. Add to the potato mixture and toss to coat. Season to taste with salt and pepper. Serve warm or at room temperature.
nutrition information (per serving):
Photo: Scott Phillips