Cut the eggplants crosswise into ½-inch-thick slices and sprinkle the cut sides with 1½ teaspoons of salt.

Place the eggplant slices in a single layer on paper towels and let them stand for 1 hour.

Cut the zucchini and squash lengthwise into ⅛ to ¼-inch-thick slices and set them aside.

In a food processor, combine ½ teaspoon of salt, ½ cup of olive oil, minced garlic, ¼ cup of chopped fresh basil, 2 tablespoons of chopped mint, and 6 tablespoons of balsamic vinegar.

Stop to scrape down the sides as needed.

Rinse the eggplant slices with water and pat them dry.

Lightly brush the slices with the olive oil mixture and sprinkle with ¼ teaspoon of salt.

Coat the cold grill grate with cooking spray and place it on the grill over medium-high heat (350° to 400°).

Put the eggplant on the grate and grill, covered with the lid, for 10 to 12 minutes or until lightly browned, turning occasionally and lightly brushing with the olive oil mixture.

Remove the eggplant from the grill.

Sprinkle the zucchini and squash slices with the remaining ¼ teaspoon of salt and lightly brush them with the olive oil mixture.

Place the slices on the lightly greased grill grate.

Grill the zucchini and squash slices, covered with the grill lid, over medium-high heat for 5 minutes.

Turn them, brush with the olive oil mixture, and grill for an additional 2 minutes.

Arrange the grilled eggplant, zucchini, and squash on a serving platter.

Drizzle them with the remaining olive oil mixture.

Garnish with fresh basil sprig if desired.