Thread the onion rounds from side to side onto two metal skewers so the rings stay intact during grilling. Brush both the onions and the zucchini halves with oil, then season evenly with salt and pepper.

Whisk the remaining oil, lemon zest, lemon juice, garlic, mustard, and salt together in a small bowl until the dressing is well combined.

Prepare the grill for direct cooking. If using charcoal, light a large chimney starter half-filled with briquettes; when they are covered with ash, spread them evenly and heat the grate for 5 minutes. If using gas, heat all burners on high for 15 minutes, then reduce the heat to medium.

Clean and oil the cooking grate. Place the vegetables on the grill, cut-side down. Cook (covered if using gas) for 18 to 22 minutes, turning as needed, until the vegetables are tender and deeply caramelized. Transfer them to a platter as they finish cooking.

Remove the skewers from the onions and discard any excessively charred outer rings. Whisk the dressing once more to recombine, drizzle it over the warm vegetables, and sprinkle with fresh basil. Serve warm.