Scoop balls of flesh from the center of the zucchini to create boats (see tip for help); reserve the flesh balls. Preheat a grill to medium-high.
Heat 1 tbsp. EVOO in a large skillet over medium heat; add the onion and cook for 5 minutes. Stir in the garlic and cook for 1 minute. Add the remaining 2 tbsp. EVOO, the eggplant and zucchini balls; cover and cook for 8 minutes. Add the tomatoes and cook, stirring, until the mixture is thick, about 5 minutes. Stir in the parsley; season with salt and pepper.
Fill the zucchini shells with the ratatouille, sprinkle with the cheese and grill, covered, over medium-high until the cheese is melted and the shells are slightly softened.