Cut the onions lengthwise into 1-inch thick wedges, leaving the layers of each wedge attached at the root end. Gently toss the onion wedges with 1 Tbsp. olive oil, reserving the rest of the oil for the dressing.
Arrange the onion wedges on a grill over medium heat and cover with an inverted foil pan. Grill until tender (about 15 – 20 minutes), turning occasionally to ensure even cooking.
While the onions are cooking, prepare the dressing. Combine the vinegar, garlic, and oregano in a small bowl. Add the remaining olive oil in a slow steady stream, whisking continuously.
Toss the onions with the dressing, and season to taste with salt and pepper.