Prepare an ice water bath and set it near the stove. Bring a small pot of water to a vigorous boil and immerse just the bulbs of the onions in the boiling water, taking care to keep the greens from drooping over onto the burner. Cook the bulbs for 3 minutes, then plunge them into the ice water to stop the cooking. Pat the onions dry and cut them in half lengthwise, from the tops of the greens through the bulbs. In a bowl, toss the onions with 1 tablespoon of the olive oil and season with kosher salt to taste.
Get a grill lit and let it warm up, or let the coals cook down, while you make the romesco sauce: In a blender, combine the garlic, pecans, peppers, tomato, cayenne, paprika, and vinegar and pulse until just beginning to get smooth. Turn the blender on low speed and drizzle in the remaining 2 tablespoons olive oil, and then finish by adding the yogurt and seasoning with kosher salt to taste. Blend well and set aside.
