Preheat the a gas or charcoal grill on medium high heat.
Slice the top off the garlic, so the cloves are visible. Drizzle with 1 teaspoon olive oil and sprinkle with a pinch of salt and pepper. On a piece of aluminum foil, grill the garlic cut side down for 3 minutes before wrapping it in a loose foil packet. Move to a cooler spot on the grill over indirect heat. Grill for 25-30 minutes until the cloves are tender.
While the garlic is cooking, toss the eggplant, corn and tomatoes with 1 tablespoon olive oil, 1 teaspoon kosher salt and 1/4 teaspoon black pepper. Grill the corn until it is lightly charred about 5-7 minutes. Grill the eggplant and tomatoes until they have grill marks, the eggplant is tender and the tomatoes are juicy, about 4 minutes per side.
When they are cool enough to handle, slice the corn off the cobs and roughly chop the tomatoes, discarding any loose skins.
In a small bowl, mash 2-3 garlic cloves into a paste. Whisk in the white wine vinegar, 3 tablespoons olive oil, 1/4 teaspoon salt and 1/4 teaspoon black pepper.
In a large bowl, combine the eggplant, corn, tomatoes, scallions and arugula and fold in the garlic vinaigrette.
Notes
Extra garlic cloves can be used as a spread on bread, in pasta or on pizza.