Before serving heat oven to 350F. If using a charcoal grill, start the coals and get the grill heated. Or if using a gas grill wait until zucchini and eggplant have been layered to dry.
Lightly salt the zucchini and eggplant slices. Layer the salted slices on double thickness of paper towels, so they are laying flat, adding layers of paper towels as needed. Finish layering by covering with a double thickness of paper towels and press flat with the bottom of a heavy pan or platter to squeeze out the moisture.
Let the eggplant and zucchini rest for 15 minutes. Brush zucchini, eggplant, peppers, and onion with oil. Grill the vegetables for 3 - 8 minutes until done. Core and seed the peppers and cut into thick slices. Cut the eggplant, zucchini and onion into 1" thick slices. Arrange the sliced vegetables on a platter. Whisk olive oil, paprika and garlic and drizzle over the vegetables. Sprinkle with parsley. Serve with crusty bread slices.