Putonion rounds, from side to side, onto 2 metal skewers. Brush onion and zucchini evenly with ¼ cup olive oil and season with 2 teaspoons kosher salt (or 1 teaspoon table salt) and pepper to taste.
Whisk remaining 2 tablespoons olive oil, garlic, lemon zest and juice, mustard, and ½ teaspoon kosher salt (or ¼ teaspoon table salt) together in small bowl; set aside.
Grill vegetables over medium heat, turning once, until tender and caramelized, 18 to 22 minutes (move vegetables as needed to ensure even cooking). Transfer vegetables to platter; remove skewers from onion and discard any charred outer rings. Rewhisk vinaigrette and pour over vegetables. Sprinkle with basil and serve.