In small bowl, stir all aioli ingredients until well mixed. Cover and refrigerate at least 1 hour before serving.
Heat coals or gas grill for direct heat.
In large bowl, toss vegetables with oil and salt. Heat grill basket (grill “wok”) on grill until hot. Add vegetables to grill basket. Cover and grill vegetables 6 to 10 minutes, shaking basket or stirring vegetables occasionally, until vegetables are crisp-tender and lightly charred.
Arrange salami around edge of large serving platter. Mound grilled vegetables onto center of serving platter. Sprinkle cheese cubes over vegetables. Serve with aioli for dipping.