How to Make It
Place potatoes in a large saucepan; cover with water by 2 inches. Bring to a boil over high; reduce heat to medium, and simmer until just tender, about 10 minutes. Drain in a colander; rinse under running water to cool. Halve lengthwise.
Heat a grill pan over high. Coat with cooking spray. Place potatoes, cut side down, on pan. Grill until potatoes are lightly charred, 2 to 3 minutes per side. Transfer to a large bowl.
Combine parsley, oil, vinegar, shallots, oregano, crushed red pepper, and 1/4 teaspoon of the salt in a small bowl. Add to potatoes, and toss to coat. Sprinkle potatoes with remaining salt.
Alternative Step 2 (Grilling): Preheat grill to high (450°F to 500°F). Coat grate with cooking spray. Place potatoes, cut side down, on oiled grates; grill, uncovered, until lightly charred, 2 to 3 minutes per side. Transfer to a large bowl.