Preheat grill for medium heat and lightly oil the grate.

Toss asparagus, eggplant, and tomatoes with about 1/2 teaspoon salt.

Arrange vegetables on the preheated grill; cook until tender, 5 to 7 minutes per side.

Whisk olive oil and vinegar in a bowl until smooth; season to taste with salt and black pepper. Toss romaine, endive, and dressing together in a large bowl.

Serve grilled vegetables atop the dressed lettuce mixture; sprinkle with Parmesan cheese.