Preheat grill to medium-high heat for direct heat grilling. Cut eggplant, zucchini, and squash in half longwise. For the eggplant, also cut off some over the outer skin so both sides of the eggplant are flat. Drizzle veggies liberally with olive oil and season with salt and pepper.
Grill vegetables over medium-high heat for 3-5 minutes on both sides until the veggies have nice grill marks and are just tender. The eggplant might need a few extra minutes until it’s tender.
Remove veggies from grill and slice into rounds.
Make pizzas by laying out thin crust pizzas and top with about 1/4 cup of pizza sauce per pizza. Sprinkle with mozzarella (about 2-3 oz. per pizza) and spread chopped, grilled veggies in an even layer. Finish pizzas with Parmesan, a pinch of dried oregano, and a pinch of salt and pepper.
Transfer pizzas to a hot grill. Cover and grill for 5-6 minutes until the pizzas are very crispy around the edges and the toppings are bubbling.
Remove pizzas and let cool for a minute. Then garnish with scallions and serve immediately.